5 2 3

We also multiply the denominators 5 x 7 to get the denominator for the answer, For example, if the number is 2 1/3, you will need to change this to 7/3. Intermittent fasting is an eating pattern that involves regular fasting. The 5:2 diet, also known as The Fast Diet, is currently the most. What happens when you need to compare fractions with different bottom numbers? For example, which of these is larger: 2/3 or 1/5? It's difficult to tell just by.

: 5 2 3

5 2 3
5 2 3
5 2 3

For a calculation that has only one mathematical operation with two numbers, it is a simple case of either adding, subtracting, multiplying or dividing to find your answer.

But what about when there are several numbers, and different operations? Maybe you need to divide and multiply, or add and divide. What do you do then?

Fortunately, mathematics is a logic-based discipline. As so often, there are some simple rules to follow that help you work out the order in which to do the calculation. These are known as the ‘Order of Operations’.


Rules of Ordering in Mathematics - BODMAS

BODMAS - Rules of Ordering in Mathematics. Brackets, Orders, Division, Multiplication, Addition and Subtraction.

BODMAS is a useful acronym that tells you the order in which you solve mathematical problems. 5 2 3 important that you follow the rules of BODMAS, because without it your answers can be wrong.

The BODMAS acronym is for:

  • Brackets (parts of a calculation inside brackets always come first).
  • Orders (numbers involving powers or square roots).
  • Division.
  • Multiplication.
  • Addition.
  • Subtraction.

BODMAS, BIDMAS or PEMDAS?


You may often see BIDMAS instead of BODMAS. They are exactly the same. In BIDMAS, the ‘I’ refers to Indices, which are the same as Orders. For more information, see our page on Special Numbers and Concepts.


PEMDAS

PEMDAS is commonly used the in USA it works 5 2 3 same as BODMAS. The PEMDAS acronym is:

Parentheses,

Exponents (powers and roots),

Multiplication and Division,

Addition and Subtraction.



Further Reading from Skills You Need


The Skills You Need Guide to Numeracy

The Skills You Need Guide to Numeracy

Skills You Need

This four-part guide takes you through the basics of numeracy from arithmetic to algebra, with stops in between at fractions, decimals, geometry and statistics.

Whether you want to brush up on 5 2 3 basics, or help your children with their learning, this is the book for you.


Using BODMAS

Brackets

Start with anything inside brackets, going from left to right.

Example:

4 × (3 + 2) = ?

You need to do the operation, inside the brackets first, 3 + 2, then multiply the answer by 4.

3 + 2 = 5.
4 × 5 = 20

If you ignored the brackets and did your calculation from left to right 4 × 3 + 2 you would get 14. You can see how the brackets make a difference to the answer.

Orders

Do anything involving a power or a square root next (these are also known as orders), again working from left to right if there is more than one.

Example:

32 + 5 = ?

You need to calculate the power first, before you can add 5.

32 = 3 × 3 = 9
9 + 5 = 14

Division and Multiplication

Once you have done any parts of the calculation involving brackets or powers the next step is division and multiplication.

Multiplication and division rank equally, so you work from left to right in the sum, doing each operation in the order in which it appears.

Example:

6 ÷ 2 + 7 × 4 = ?

You need to do division and multiplication first, but you have one of each.

Start from the left and work across to the right, which means that you start with 6 ÷ 2 = 3. Then do the multiplication, 7 × 4 = 28.

Your calculation is now 3 + 28.

Complete the addition calculation to find the answer, 31.

See our pages: Multiplication and Division for more.

Addition and Subtraction

The final step is to calculate any addition or subtraction. Again, subtraction and addition rank equally, and you simply work from left to right.

Example:

4 + 6 − 7 + 3 = ?

You start on the left and work your way across.

4 + 6 = 10
10 − 7 = 3
3 + 3 = 6
The answer is 6.

See our pages: Addition and Subtraction for more.

Bringing It All Together

This final worked example includes all elements of BODMAS.

Example:

4 + 82 × (30 ÷ 5) = ?

Start with the calculation inside the brackets.

30 ÷ 5 = 6
This gives you 4 + 82 × 6 = ?

Then calculate the orders - in this case the square of 8.

82 = 64
Your calculation is now 4 + 64 × 6

Then move to the multiplication 64 × 6 = 384

Finally perform the addition. 4 + 384 = 388

The answer is 388.



BODMAS Test Questions

The rules of BODMAS are easiest to understand with some practice and examples.

Try these calculations yourself and then open up the box (click on the + symbol to the left) to see the workings and answers.

There are no brackets or orders in this calculation.

  1. Multiplication comes before addition, so start with 20 × tcf bank chicago routing number = 60.
  2. The calculation now reads 3 heritage federal credit union newburgh 60

The answer is therefore 63.

  1. Start with brackets. (3 + 2) = 5.
  2. The calculation now reads 25 − 5 ÷ 5
  3. Division comes before subtraction. 5 ÷ 5 = 1.
  4. The calculation now reads 25 − 1

The answer is therefore 24.

  1. Start with brackets. (1+10) = 11.
  2. The calculation now reads 10 + 6 × 11
  3. Multiplication comes before addition. 6 × 11 = 66.
  4. The calculation now reads 10 + 66.

The answer is therefore 76.

When there is no sign like in this calculation, the operator is a multiplication, the same as writing 5 × (3 + 2) + 52.

  1. Complete the calculation inside the brackets first: (3 + 2) = 5.
  2. That gives you 5 × 5 + 52.
  3. The next step is orders, in this case, the square. 52 = 5 × 5 = 25. Now you have 5 × 5 + 25.
  4. Division and multiplication come before addition and subtraction, so your next step is 5 × 5 = 25. Now the calculation reads 25 + 25 = 50.

The answer is 5 2 3 one has everything! But don’t panic. BODMAS still applies, and all you have to do is unpick the calculation.

  1. Start with brackets. (105 + 206) = 311.
  2. The calculation now reads 311 – 550 ÷ 52 + 10
  3. Next, orders or powers. In this case, that’s 52 = 25.
  4. The calculation now reads 311 – 550 ÷ 25 + 10
  5. Next, division and multiplication. There is no multiplication, but the division is 550 ÷ 25 = 22.
  6. Now the calculation reads 311 – 22 + 10.
  7. Although you still have two operations left, addition and subtraction rank equally, so you just go from left to right. 311 – 22 = 289, and 289 + 10 = 299.

The answer is 299.

Problems like this often do the rounds on social media sites, with captions like '90% of people get this wrong'. Just follow the rules of BODMAS to get the correct answer.

  1. There are no brackets or orders so start with division and multiplication.
  2. 7 ÷ 7 = 1 and 7 × 7 = 49.
  3. The calculation now reads 7 + 1 + 49 – 7
  4. Now do the addition and subtraction. 7 + 1 + 49 = 57 – 7 = 50

The answer is therefore 50.


How Did You Do?

Hopefully you managed to get all the answers right. If not, go back and review where you went wrong, and read over the rules again.

The more you practise, the easier BODMAS becomes and eventually you won’t even have to think about it.

Источник: https://www.skillsyouneed.com/num/bodmas.html

Exponents

The exponent of a number says how many times to use the number in a multiplication.

 

8 to the Power 2

In 82 the "2" says to use 8 twice in a multiplication,
so 82 = 8 × 8 = 64

In words: 82 could be called "8 to the power 2" or "8 to the second power", or simply "8 squared"

Exponents are also called Powers or Indices.

Some more examples:

Example: 53 = 5 × 5 × 5 = 125

  • In words: 53 could be called "5 to the third power", "5 to the power 3" or simply "5 cubed"

Example: 24 = 2 × 2 × 2 × 2 = 16

  • In words: 24 could be called "2 to the fourth power" or "2 to the power 4" or simply "2 to the 4th"

 

Exponents make it easier to write and use many multiplications

Example: 96 is easier to write and read than 9 × 9 × 9 × 9 × 9 × 9

You can multiply any number by itself as many times as you want using exponents.

Try here:

algebra/images/exponent-calc.js

So in general:

an tells you to multiply a by itself,
so there are n of those a's:
 exponent definition

Another Way of Writing It

Sometimes people use the ^ symbol (above the 6 on your keyboard), as it is easy to type.

Example: 2^4 is the same as 24

Negative Exponents

Negative? What could be the opposite of multiplying? Dividing!

So we divide by the number each time, which is the same as multiplying by 1number

Example: 8-1 =18 = 0.125

We can continue on like this:

Example: 5-3 = 15 × 15 × 15 = 0.008

But it is often easier to do it this way:

5-3 could also be calculated like:

15 × 5 × 5 = 153 = 1125 = 0.008

Negative? Flip the Positive!

negative-exponent

That last example showed an easier way to handle negative exponents:

  • Calculate the positive exponent (an)
  • Then take the Reciprocal (i.e. 1/an)

More Examples:

Negative Exponent Reciprocal of
Positive Exponent
 Answer
4-2 = 1 / 42 = 1/16 = 0.0625
10-3 = 1 / 103 = 1/1,000 = 0.001
(-2)-3 = 1 / (-2)3 = 1/(-8) = -0.125

What if the Exponent is 1, or 0?

1 If the exponent is 1, then you just have the number itself (example 91 = 9)
   
0 If the exponent is 0, then you get 1 (example 90 = 1)
   
  But what about 00 ? It could be either 1 or 0, and so people say it is "indeterminate".

It All Makes Sense

If you look at that table, you will see that positive, zero or negative exponents are really part of the same (fairly simple) pattern:

Example: Powers of 5 2 3. etc. exponent 5 times larger or smaller
525 × 525
5155
5011
5-1150.2
5-215 × 150.04
 . etc. 

Be Careful About 5 2 3 avoid confusion, use parentheses () in cases like this:

With () :(−2)2 = (−2) × (−2) = 4
Without () :−22 = −(22) = −(2 × 2) = −4

With () :(ab)2 = ab × ab
Without () :ab2 = a × (b)2 = a × b × b

 

305, 1679, 306, 1680, 1077, 1681, 1078, 1079, 3863, 3864

Laws of ExponentsFractional Bb gun sniper scope of 10DecimalsMetric Numbers

Источник: https://www.mathsisfun.com/exponent.html

How to Find the General Term of Sequences

Ray is a licensed engineer in the Philippines. He loves to write about mathematics and civil engineering.

What Is a Sequence?

A sequence is a function whose domain is an ordered list of numbers. These numbers are positive integers starting with 1. Sometimes, people mistakenly use the terms series and sequence. A sequence is a set of positive integers while series is the sum of these positive integers. The denotation for the terms in a sequence is:

a1, a2, a3, a4, an. . .

Finding the nth term of a sequence is easy given a general equation. But doing it the other way around is a struggle. Finding a general equation for a given sequence requires a lot central illinois bank hours thinking and practice but, learning the specific rule guides you in discovering the general equation. In this article, you will learn how to induce the patterns of sequences and write the general term when given the first few terms. There is a step-by-step guide for you to follow and understand the process and provide you with clear and correct computations.

What Is an Arithmetic Sequence?

An arithmetic series is a series of ordered numbers with a constant difference. In an arithmetic sequence, you will observe that each pair of consecutive terms differs by the same amount. For example, here are the first five terms of the series.

3, 8, 13, 18, 23

Do you notice a special pattern? It is obvious that each number after the first is five more than the preceding term. Meaning, the common difference of the sequence is five. Usually, the formula for the nth term of an arithmetic sequence whose first term is a1 and whose common difference is d is displayed below.

an = a1 + (n - 1) d

Steps in Finding the General Formula of Arithmetic and Geometric Sequences

1. Create a table with headings n and an where n denotes the set of consecutive positive integers, and an represents the term corresponding to the positive integers. You may pick only the first five terms of the sequence. For example, tabulate the series 5, 10, 15, 20, 25. . .

2. Solve the first common difference of a. Consider the solution as a tree diagram. There are two conditions for this step. This process applies only to sequences whose nature are either linear or quadratic.

Condition 1: If the first common difference is a constant, use the linear equation ax + b = 0 in finding the general term of the sequence.

a. Pick two pairs of numbers from the table and form two equations. The value of n from the table corresponds to the x in the linear equation, and the value of an corresponds to the 0 in the linear equation.

a(n) + b = an

b. After forming the two equations, calculate a and b using the subtraction method.

c. Substitute a and b to the general term.

d. Check if the general term is correct by substituting the values in the general equation. If the general term does not meet the sequence, there is an error with united petsafe phone number calculations.

Condition 2: If the first difference is not constant and the second difference is constant, use the quadratic equation ax2 + b(x) + c = 0.

a. Pick three pairs of numbers from the table and form three equations. The value of n from the table corresponds to the x in the linear equation, and the value of an corresponds to the 0 in the linear equation.

an2 + b(n) + c = an

b. After forming the three equations, calculate a, b, and c using the subtraction method.

c. Substitute a, b, and c to the general term.

d. Check if the general term is correct by substituting the values in the general equation. If the general term does not meet the sequence, there is an error with your calculations.

Problem 1: General Term of an Arithmetic Sequence Using Condition 1

Find the general term of the sequence 7, 9, 11, 13, 15, 17. .

Solution

a. Create a table of an and n values.

b. Take the first difference of an.

c. The constant difference is 2. Since the first difference is a constant, therefore the general term of the given sequence is linear. Pick two sets of values from the table and form two equations.

General Equation:

an + b = an

Equation 1:

at n = 1, a1 = 7

a (1) + b = 7

a + b = 7

Equation 2:

at n = 2a2 = 9

a (2) + b = 9

2a + b = 9

d. Subtract the two equations.

(2a + b = 9) - (a + b = 7)

a = 2

e. Substitute the value of a = 2 in equation 1.

a + b = 7

2 + b = 7

b = 7 - 2

b = 5

f. Substitute the values a = 2 and b = 5 in the general equation.

an + b = an

2n + 5 = an

g. Check the general term by substituting the values into the equation.

an = 2n + 5

a1= 2(1) + 5 = 7

a2= 2(2) + 5 = 9

a3= 2(3) + 5 = 11

a4= 2(4) + 5 = 13

a5= 2(5) + 5 = 15

a6= 2(6) + 5 = 17

Therefore, the general term of the sequence is:

an = 2n + 5

Problem 2: General Term of Arithmetic Sequence Using Condition 2

Find the general term of the sequence 2, 3, 5, 8, 12, 17, 23, 30. .

Solution

a. Create a table of an and 5 2 3 values.

b. Take the first difference of an. If the first difference of an is not constant, take the second.

c. The second difference is 1. Since the second difference is a constant, therefore the general term of the given sequence is quadratic. Pick three sets of values from the table and form three equations.

General Equation:

an2 + b(n) + c = an

Equation 1:

at n = 1, a1 = 2

a (1) + b (1) + c = 2

a + b + c = 2

Equation 2:

at n = 2, a2 = 3

a (2)2 + b (2) + c = 3

4a + 2b + c = 3

Equation 3:

at n = 3, a2 = 5

a (3)2 + b (3) + c = 5

9a + 3b + c = 5

d. Subtract the three equations.

Equation 2 - Equation 1: (4a + 2b + c = 3) - (a + b + c = 2)

Equation 2 - Equation 1: 3a + b = 1

Equation 3 - Equation 2: (9a + 3b + c = 5) - (4a + 2b + c = 3)

Equation 3 - Equation 2: 5a + b = 2

(5a + b = 2) - (3a + b = 1)

2a = 1

a = 1/2

e. Substitute the value of a = 1/2 in any of the last two equations.

3a + b = 1

3 (1/2) + b = 1

b = 1 - 3/2

b = - 1/2

a + b + c = 2

1/2 - 1/2 + c = 2

c = 2

f. Substitute the values a = 1/2, b = -1/2, and c = 2 in the general equation.

an2 + b(n) + c define straight ally an

(1/2)n2 - (1/2)(n) + 2 = an

g. Check the general term by substituting the values into the equation.

(1/2)n2 - (1/2)(n) + 2 = an

an = 1/2 (n2 - n + 4)

a1 = 1/2 (12 - 1 + 4) = 2

a2 = 1/2 (22 - 2 + 4) = 3

a3 = 1/2 (32 - 3 + 4) = 5

a4 = 1/2 (42 - 4 + 4) = 8

a5 = 1/2 (52 - 5 + 4) = 12

a6 = 1/2 (62 - 6 + 4) = 17

a7 = 1/2 (72 - 7 + 4) = 23

Therefore, the general term of the sequence how to cancel walmart pickup order = 1/2 (n2 - n + 4)

Problem 3: General Term of Arithmetic Sequence Using Condition 2

Find the general term for the sequence 2, 4, 8, 14, 22. . .

Solution

a. Create a table of an and n values.

b. Take the first and second difference of an.

c. The second difference is 2. Since the second difference is a constant, therefore the general term of the given sequence is quadratic. Pick three sets of values from the table and form three equations.

General Equation:

an2 + b(n) + c = an

Equation 1:

at n = 1, a1 = 2

a (1) + b (1) + c = 2

a + b + c = 2

Equation 2:

at n = 2, a2 = 4

a (2)2 + b (2) + c = 4

4a + 2b + c = 4

Equation 3:

at n = 3, a2 = 8

a (3)2 + b (3) + c = 8

9a + 3b + c = 8

d. Subtract the three equations.

Equation 2 - Equation 1: (4a + 2b + c = 4) - (a + b + c = 2)

Equation 2 - Equation 1: 3a + b = 2

Equation 3 - Equation 2: (9a + 3b + c = 8) - (4a + 2b + c = 4)

Equation 3 - Equation 2: 5a + b = 4

(5a + b = 4) - (3a + b = 2)

2a = 2

a = 1

e. Substitute the value of a = 1 in geld overmaken naar creditcard ics abn amro of the last two equations.

3a + b = 2

3 (1) + b = 2

b = 2 - 3

b = - 1

a + b + c = 2

1 - 1 + c = 2

c = 2

f. Substitute the values a = 1, b = -1, and c = 2 in the general equation.

an2 + b(n) + c = an

(1)n2 - (1)(n) + 2 = an

n2 - n + 2 = an

g. Check the general term by substituting the values into the equation.

n2 - n + 2 = an

a1 = 12 - 1 + 2 = 2

a2 = 22 - 2 + 2 = 4

a3 = 32 - 3 + 2 = 8

a4 = 42 - 4 + 2 = 14

a5 = 52 - 5 + 2 = 22

Therefore, the general term of the sequence is:

an = n2 - n + 2

Self-Assessment

For each question, choose the best answer. The answer key is below.

  1. Find the general term of the sequence 25, 50, 75, 100, 125, 150. .
    • an = n + 25
    • an = 25n
    • an = 25n^2
  2. Find the general term of the sequence 7/2, 13/2, 19/2, 25/2, 31/2.
    • an = 3 + n/2
    • an = n + 3/2
    • an = 3n + 1/2

Answer Key

  1. an = 25n
  2. an = 3n + 1/2

Interpreting Your Score

If you got 0 correct answers: Sorry, try again!

If you got 2 correct answers: Good Job!

Explore Other Math Articles

Questions & Answers

Question: How to find general term of sequence 0, 3, 8, 15, 24?

Answer: The general term for the sequence is an = a(n-1) + 2(n+1) + 1

Question: whats is the general term of the set {1,4,9,16,25}?

Answer: The general term of the sequence {1,4,9,16,25} is n^2.

Question: How do I get the formula if the common difference falls on the third row?

Answer: If the constant difference falls on the third, the equation is a cubic. Try solving it following the pattern for quadratic equations. If it's not applicable, you can solve it using logic and some trial and error.

Question: How to find general term of the sequence 4, 12, 26, 72, 104, 142, 186?

Answer: The general term of the sequence is an = 3n^2 − n + 2. The sequence is quadratic with second difference 6. The general term has the form an = αn^2+βn+γ.To find α, β, γ plug in values for n = 1, 2, 3:

4 = α + β + γ

12 = 4α + 2β + γ

26 = 9α + 3β + γ

and solve, yielding α = 3, β = −1, γ = 2

Question: Is there a faster way to calculate the general term of a sequence?

Answer: Unfortunately, this is the easiest method in finding the general term of basic sequences. You can refer to your textbooks or wait until I get to write another article regarding your concern.

Question: What will be nth term of the sequence 4, 12, 28, 46, 72, 104, 142 .?

Answer: Unfortunately, this sequence does not exist. But if you replace 28 with 26. The general term of the sequence would be an = 3n^2 − n + 2

Question: What is the explicit formula for the nth term of the sequence 1,0,1,0?

Answer: The explicit formula for the nth term of the sequence 1,0,1,0 is an = 1/2 + 1/2 (−1)^n, wherein the index starts at 0.

Question: What is the set builder notation of an empty set?

Answer: The notation for an empty set is "Ø."

Question: What is the general formula of the sequence 3,6,12, 24.?

Answer: The general term of the given sequence 5 2 3 an = 3^r^(n-1).

Question: What if there is no common difference for all the rows?

Answer: if there is no common difference for all the rows, try to identify the flow of the sequence through trial and error method. You must identify the pattern first before concluding an equation.

Question: What 5 2 3 the general term of sequence 6,1,-4,-9?

Answer: This is a simple arithmetic sequence. It follows the formula an = a1 + d(n-1). But in this case, the second term has to be negative an = a1 - d(n-1).

At n = 1, 6 - 5(1-1) = 6

At n = 2, 6 - 5(2-1) = 1

At n = 3, 6 - 5(3-1) = -4

At n = 4, 6 - 5(4-1) = -9

Question: What is the general form of the sequence 5,9,13,17,21,25,29,33?

Answer: The general term of the sequence is 4n + 1.

Question: Is there another way of finding general term of sequences using condition 2?

Answer: There are a lot of ways in solving the general term of sequences, one is trial and error. The basic thing to do is writing down their commonalities and derive equations from those.

Question: How to find the general term for the sequence 1/22/3 ,3/4 ,4/5.?

Answer: For the given sequence the general term could be defined as n/(n + 1), where ’n’ is clearly a natural number.

Question: How do i find the general term of a sequence 9,9,7,3?

Answer: If this is the correct sequence, the only pattern I see is when you start with number 9.

9

9 - 0 = 9

9 - 2 = 7

9 - 6 = 3

Therefore. 9 - (n(n-1)) where n starts with 1.

If not, I believe there is a mistake with the sequence you provided. Please try to recheck it.

Question: How to find an expression for the general term of american fidelity mortgage corp series 1+1•3+1•3•5+1•3•5•7+.?

Answer: The general term of the series is (2n-1)!.

Question: Amazon chime video term for the sequence {1,4,13,40,121} ?

Answer: 1

1+3 = 4

1+3+3^2 = 13

1+3+3^2+3^3 = 40

1+3+3^2+3^3+3^4 = 121

So, the general term of the sequence is a(sub)n=a(sub)n-1 + 3^(n-1)

Question: How to find general term for sequence given as an=3+4a(n-1) given a1=4?

Answer: So you mean how to find the sequence given the general term. Given the general term, just start substituting the value of a1 in the equation and let n =1. Do this for a2 where n=2 and so on and so forth.

Question: How to find general pattern of 3/7, 5/10, 7/13.?

Answer: For fractions, you can separately analyze the pattern in the numerator and the denominator.

For the numerator, we can see that the pattern is by adding 2.

3

3 + 2 = 5

5 + 2 = 7

or by adding multiples of 2

3

3 + 2 = 5

3 + 4 = 7

Therefore the general term for the numerator is 2n + 1.

For the denominator, we can observe that the pattern is by adding 3.

7

7 + 3 = 10

10 + 3 = 13

Or by adding multiples of 3

7

7 + 3 = 10

7 + 6 = 13

Therefore, the pattern for the denominator is 3n + 4.

Combine the two patterns and you'll come up with (2n + 1) / (3n + 4) which is the final answer.

Question: What is the general term of the sequence {7,3,-1,-5}?

Answer: The pattern for the given sequence is:

7

7 - 4 = 3

3 - 4 = -1

-1 - 4 = -5

All succeeding terms are subtracted by 4.

Question: How to find the general term of the sequence 8,13,18,23.?

Answer: First thing to do is try to find a common difference.

13 - 8 = 5

18 - 13 = 5

23 - 18 = 5

Therefore the common difference is 5. The sequence is done by adding 5 to the previous term. Recall that the formula for the arithmetic progression is an = a1 + (n - 1)d. Given a1 = 8 and d = 5, substitute the values to the general formula.

an = a1 + (n - 1)d

an = 8 + (n - 1) (5)

an = 8 + 5n - 5

an = 3 + 5n

Therefore, the general term of the arithmetic sequence is an = 3 + 5n

Question: How to find general term of sequence of -1, 1, 5, 9, 11?

Answer: I actually don't get the sequence really well. But my instinct says it goes like this.

-1 + 2 = 1

1 + 4 = 5

5 +4 = 9

9 + 2 = 11

+2, +4, +4, +2, +4, +4, +2, +4, +4

Question: How to find the general term of 32,16,8,4,2.?

Answer: I believe each term (except the first term) is found by dividing the previous term by 2.

Question: How to find general term of sequence 1/2, 1/3, 1/4, 1/5?

Answer: You can observe that the only changing portion is the denominator. So, we can set the numerator as 1. Then the common difference of the denominator is 1. So, the expression is n+1.

The general term of the sequence is 1/(n+1)

Question: How to find general term of the sequence 1,6,15,28?

Answer: The general term of the sequence is n(2n-1).

Question: How to pay a simple mobile phone bill to find the general term of the sequence 1, 5, 12, 22 ?

Answer: The general term of the sequence 1, 5, 12, 22 is [n(3n-1)]/2.

© 2018 Ray

Comments

Ray (author) from Philippines on April 24, 2020:

Hi, Earnest. I am currently working on my new blogs to be featured on my own website. It'll include topics related to geometric series, geometric sequences, arithmetic series, and arithmetic sequences. There'll be also topics about harmonic series and geometric infinite series. Please send me your e-mail so I can send you an e-mail as soon as my website is up. You may visit my profile to check on my social media and e-mail. Thanks!

Earnest on April 24, 2020:

. some GPs please and also sequences of this kind .1/27+2/37+3/47+4/47+.and Any personal technique could help so much. Homes for sale reno nv mls for the service!

Ray (author) from Philippines on March 08, 2020:

For those who want to learn finding the nth term of arithmetic sequences and geometric sequences, please leave your comments here in the comment section. Thank you!

Ray (author) from Philippines on January 04, 2020:

Technically, the sequences you provided are not basic sequences and requires an advanced knowledge in the field of mathematics. For instance, the general term of the sequence 1,3,11,43… is n! multiplied by the summation of 1/(n-k) where k starts with 0. Soon, I’ll create an article discussing about these type of sequences.

Akinwunmi Sulaiman Awwal on December 16, 2019:

how to get general term for the sequence

3, 10, 22, 35, 49,

2, 10, 25, 54,

2, 5, 11, 23, 38,

1, 3, 11, 43,

1, 2, 5, 15, 54,

1, 4, 13, 47, 185,

Bitaniya bahiru on October 16, 2019:

Thank you so much. it's very helpful

syed ashar ali on September 18, 2019:

I want to find a generalized term of a sequence whose common ratio is an arithmetic sequence

Nasibud Din on August 25, 2019:

I am not understand dicemal and binary system

godfrey sebabatso mokatile on August 18, 2019:

the maths has no problem is need to practice it

Brian.sitton@ciy.com on June 30, 2019:

I think in the first picture the -1 should be a +1.

(in the +7 sequence)

Jonh paul Sallaya on June 12, 2019:

General term

An.sqaure. + bn + c = An

A=1 ,b=1, c= -1

Then whats next pls?

Han on March 18, 2019:

7,13,25,49……

7=6+1=6x2^0+1

13=6x2+1=6x2^1+1

25=6x4+1=6x2^2+1

49=6x8+1=6x2^3+1……So:

an=6x2^(n-1)+1

Cody on December 29, 2018:

Then what is the sequence for 7,13,25,49.

lol on November 02, 2018:

this really helped me, thanks

Rowan on October 21, 2018:

That arithmetic sequence is super wrong. -6 + 7 is not -1

Srijan Guha on August 27, 2018:

Easily understandable and very helpful mathematical article.

Nicole Ann Cuevas on July 21, 2018:

Thanks! Its a big help!

Ray (author) from Philippines on June 29, 2018:

Thank you, Ma'am Chitrangada Sharan. I really like to help students having trouble with their Mathematics subject. Have a great day!

Chitrangada Sharan from New Delhi, India on June 29, 2018:

Your article is educative and informative! Very well explained and useful for many.

Thanks for sharing this !

Источник: https://owlcation.com

If you're seeing this message, it means we're having trouble loading external resources on our website.

If you're behind a web m words for kindergarten, please make sure that the domains *.kastatic.org and *.kasandbox.org are unblocked.

Current time:0:00Total duration:2:26

Video transcript

We're asked to multiply 5/6 times 2/3 and then simplify our answer. So let's just multiply these two numbers. So we have 5/6 times 2/3. Now when you're multiplying fractions, it's actually a pretty straightforward process. The new numerator, or the numerator of the product, is just the product of the two numerators, or your new top number is a product of the other two top numbers. So the numerator in our product is just 5 times 2. So it's equal to 5 times 2 over 6 times 3, which is equal to-- 5 times 2 is 10 and 6 times 3 is 18, so it's equal to 10/18. And you could view this as either 2/3 of 5/6 or 5/6 of 2/3, depending on how you want to think about it. And this is 5 2 3 right answer. It is 10/18, but when you look at these two numbers, you immediately or you might immediately see that they share some common factors. They're both divisible by 2, so if we want it in lowest terms, we want to divide them both by 2. So divide 10 by 2, divide 18 by 2, and you get 10 divided by 2 is 5, 18 divided by 2 is 9. Now, you could have essentially done this step earlier on. You could've done it actually before we did the multiplication. You could've done it over here. You could've said, well, I have a 2 in the numerator and I have something divisible by 2 into the denominator, so let me divide the numerator by 2, and this becomes a 1. Let me divide the denominator by 2, and this becomes a 3. And then you have 5 times 1 is 5, and 3 times 3 is 9. So it's really the same thing we did right here. We just did it before we actually took the product. You could actually do it right here. So if you did it right over here, you'd say, well, look, 6 times 3 is eventually going to be the denominator. 5 times 2 is eventually going to be the numerator. So let's divide the numerator by 2, so this will become a 1. Let's divide the denominator by 2. This is divisible by 2, so that'll become a 3. And it'll become 5 times 1 is 5 and 3 times 3 is 9. So either way you do it, it'll work. If you do it this way, you get to see the things factored out a little bit more, so it's usually easier to recognize what's divisible by what, or you could do it who sells usa today newspaper near me the end and put things in lowest terms.
Источник: https://www.khanacademy.org/math/cc-fifth-grade-math/5th-multiply-fractions/imp-multiplying-fractions/v/multiplying-fractions

Fraction Calculator

Below are multiple fraction calculators capable of addition, subtraction, multiplication, division, simplification, and conversion between fractions and decimals. Fields above the solid black line represent the numerator, while fields below represent the denominator.


Mixed Numbers Calculator


Simplify Fractions Calculator


Decimal to Fraction Calculator


Fraction to Decimal Calculator


Big Number Fraction Calculator

Use this calculator if the numerators or denominators are very big integers.



In mathematics, a fraction is a number that represents a part of a whole. It consists of a numerator and a denominator. The numerator represents the number of equal parts of a whole, while the denominator is the total number of parts that make up said whole. For example, in the fraction of

, the numerator is 3, and the denominator is 8. A more illustrative example could 36 c to f a pie with 8 slices. 1 of those 8 slices would constitute the numerator of a fraction, while the total of 8 slices that comprises the whole pie would be the denominator. If a person were to eat 3 slices, the remaining fraction of the pie would therefore be as shown in the image to the right. Note that the denominator of a fraction cannot be 0, as it would make the fraction undefined. Fractions can undergo many different operations, some of which are mentioned below.

Addition:

Unlike adding and subtracting integers such as 2 and 8, fractions require a common denominator to undergo these operations. One method for finding a common denominator involves multiplying the numerators and denominators of all of the fractions involved by the product of the denominators of each fraction. Multiplying all of the denominators ensures that the new denominator is certain to be a multiple of each individual denominator. The numerators also need to be multiplied by the appropriate factors to preserve the value of the fraction as a whole. This is arguably the simplest way to ensure that the fractions have a common denominator. However, in most cases, the solutions to these equations will not appear in simplified form (the provided calculator computes the simplification automatically). Below is an example using this method.

+ = + =
EX: + = + = =

This process can be used for any number of fractions. Just multiply the numerators and denominators of each fraction in the problem by the product of the denominators of all the other fractions (not including its own respective denominator) in the problem.

EX:
+ + =
1×6×2
4×6×2
+
1×4×2
6×4×2
+
1×4×6
2×4×6
=
+ + = =

An alternative method for finding a common denominator is to determine the least common multiple (LCM) for the denominators, then add or subtract the numerators as one would an integer. Using the least common multiple can be more efficient and is more likely to result in a fraction in simplified form. In the example above, the denominators were 4, 6, and 2. The least common multiple is the first shared multiple of these three numbers.

Multiples of 2: 2, 4, 6, 8 10, 12
Multiples of 4: 4, 8, 12
Multiples of 6: 6, 12

The first multiple they all share is 12, so this is the least common multiple. To complete an addition (or subtraction) problem, multiply the numerators and denominators of each fraction in the problem by whatever value will make the denominators 12, then add the numerators.

EX:
+ + = + +
=

Subtraction:

Fraction subtraction is essentially the same as fraction addition. A common denominator is required for the operation to occur. Refer to the addition section as well as the equations below for clarification.

= =
EX: = = =

Multiplication:

Multiplying fractions is fairly straightforward. Unlike adding and subtracting, it is not necessary to compute a common denominator in order to multiply fractions. Simply, the numerators and denominators of each fraction are multiplied, and the result forms a new numerator and denominator. If possible, the solution should be simplified. Refer to the equations below for clarification.

EX: × = =

Division:

The process for dividing fractions is similar to that for multiplying fractions. In order to divide fractions, the fraction in the numerator is multiplied by the reciprocal of the fraction in the denominator. The reciprocal of a number a is simply

. When a is a fraction, this essentially involves exchanging the position of the numerator and the denominator. The reciprocal of the fraction would therefore be. Refer to the equations below for clarification.
/ = × =
EX: / = × = =

Simplification:

It is often easier to work with simplified fractions. As such, fraction solutions are commonly expressed in their simplified forms.

for example, is more cumbersome than. The calculator provided returns fraction inputs in both improper fraction form as well as mixed number form. In both cases, fractions are presented in their lowest forms by dividing both numerator and denominator by their greatest common factor.

Converting between fractions and decimals:

Converting from decimals to fractions is straightforward. It does, however, require the understanding that each decimal place to the right of the decimal point represents a power of 10; the first decimal place being 101, the second 102, the third 103, and so on. Simply determine what power of 10 the decimal extends to, use that power of 10 as the denominator, enter each number to the right of the decimal point as the numerator, and simplify. For example, looking at the number 0.1234, the number 4 is in the fourth decimal place, which constitutes 104, or 10,000. This would make the fraction

, which simplifies tosince the greatest common factor between the numerator and denominator is 2.

Similarly, fractions with denominators that are powers of 10 (or can be converted to powers of 10) can be translated to decimal form using the same principles. Take the fraction

for example. To convert this fraction into a decimal, first convert it into the fraction of. Knowing that the first decimal place represents 10-1, can be converted to 0.5. If the fraction were insteadthe decimal would then be 0.05, and so on. Beyond this, converting fractions into decimals requires the operation of long division.

Common Engineering Fraction to Decimal Conversions

In engineering, fractions are widely used to describe the size of components such as pipes and bolts. The most common fractional and decimal equivalents are listed below.

64th32nd16th8th4th2ndDecimalDecimal
(inch to mm)
1/64     0.0156250.396875
2/641/32    0.031250.79375
3/64     0.0468751.190625
4/642/321/16   0.06251.5875
5/64     0.0781251.984375
6/643/32    0.093752.38125
7/64     0.1093752.778125
8/644/322/161/8  0.1253.175
9/64     0.1406253.571875
10/645/32    0.156253.96875
11/64     0.1718754.365625
12/646/323/16   0.18754.7625
13/64     0.2031255.159375
14/647/32    0.218755.55625
15/64     0.2343755.953125
16/648/324/162/81/4 0.256.35
17/64     0.2656256.746875
18/649/32    0.281257.14375
19/64     0.2968757.540625
20/6410/325/16   0.31257.9375
21/64     0.3281258.334375
22/6411/32    0.343758.73125
23/64     0.3593759.128125
24/6412/326/163/8  0.3759.525
25/64     0.3906259.921875
26/6413/32    0.4062510.31875
27/64     0.42187510.715625
28/6414/327/16   0.437511.1125
29/64     0.45312511.509375
30/6415/32    0.4687511.90625
31/64     0.48437512.303125
32/6416/328/164/82/41/20.512.7
33/64     0.51562513.096875
34/6417/32    0.5312513.49375
35/64     0.54687513.890625
36/6418/329/16   0.562514.2875
37/64     0.57812514.684375
38/6419/32    0.5937515.08125
39/64     0.60937515.478125
40/6420/3210/165/8  0.62515.875
41/64     0.64062516.271875
42/6421/32    0.6562516.66875
43/64     0.67187517.065625
44/6422/3211/16   0.687517.4625
45/64     0.70312517.859375
46/6423/32    0.7187518.25625
47/64     0.73437518.653125
48/6424/3212/166/83/4 0.7519.05
49/64     0.76562519.446875
50/6425/32    0.7812519.84375
51/64     0.79687520.240625
52/6426/3213/16   0.812520.6375
53/64     0.82812521.034375
54/6427/32    0.8437521.43125
55/64     0.85937521.828125
56/6428/3214/167/8  0.87522.225
57/64     0.89062522.621875
58/6429/32    0.9062523.01875
59/64     0.92187523.415625
60/6430/3215/16   0.937523.8125
61/64     0.95312524.209375
62/6431/32    0.9687524.60625
63/64     0.98437525.003125
64/6432/3216/168/84/42/2125.4
Источник: https://www.calculator.net/fraction-calculator.html

3. An Informal Introduction to Python

3.1.3. Lists¶

Python knows a number of compound data types, used to group together other values. The most versatile is the list, which can be written as a list of comma-separated values (items) between square brackets. Lists might contain items of different types, but usually the items all have the same type.

>>> squares=[1,4,9,16,25]>>> squares[1, 4, 9, 16, 25]

Like strings (and all other built-in sequence types), lists can be indexed and sliced:

>>> squares[0]# indexing returns the item1>>> squares[-1]25>>> squares[-3:]# slicing returns a new list[9, 16, 25]

All slice operations return a new list containing the requested elements. This means that the following slice returns a shallow copy of the list:

>>> squares[:][1, 4, 9, 16, 25]

Lists also support operations like concatenation:

>>> squares+[36,49,64,81,100][1, 4, 9, 16, 25, 36, 49, 64, 81, 100]

Unlike strings, which are immutable, lists are a mutable type, i.e. it is possible to change their content:

>>> cubes=[1,8,27,65,125]# something's wrong here>>> 4**3# the cube of 4 is 64, not 65!64>>> cubes[3]=64# replace the wrong value>>> cubes[1, 8, 27, 64, 125]

You can also add new items at the end of the list, by using the method (we will see more about methods later):

>>> cubes.append(216)# add the cube of 6>>> cubes.append(7**3)# and the cube of 7>>> cubes[1, 8, 27, 64, 125, 216, 343]

Assignment to slices is also possible, and this can even change the size of the list or clear it entirely:

>>> letters=['a','b','c','d','e','f','g']>>> letters['a', 'b', 'c', 'd', 'e', 'f', 'g']>>> # replace some values>>> letters[2:5]=['C','D','E']>>> letters['a', 'b', 'C', 'D', 'E', 'f', 'g']>>> # now remove them>>> letters[2:5]=[]>>> letters['a', 'b', 'f', 'g']>>> # clear the list by replacing all the elements with an empty list>>> letters[:]=[]>>> letters[]

The built-in function also applies to lists:

>>> letters=['a','b','c','d']>>> len(letters)4

It is possible to nest lists (create lists containing other lists), for example:

>>> a=['a','b','c']>>> n=[1,2,3]>>> x=[a,n]>>> x[['a', 'b', 'c'], [1, 2, 3]]>>> x[0]['a', 'b', 'c']>>> x[0][1]'b'
Источник: https://docs.python.org/3/tutorial/introduction.html

What is 2/3 of 5?

In this article, we'll show you m words for kindergarten how to calculate 2/3 of 5 so you can work out the fraction of any number quickly and easily! Let's get to the math!

Want to quickly learn or show students how to convert 2/3 of 5? Play this very quick and fun video now!

You probably know that the number above the fraction line is called the numerator and the number below it is called the denominator. To work out the fraction of any number, we first need to convert that whole number into a fraction as well.

Here's a little tip for you. Any number can be converted to fraction if you use 1 as the add visa gift card to cash app now that we've converted 5 into a fraction, to work out the answer, we put the fraction 2/3 side by side with our new fraction, 5/1 so that we can multiply those two fractions.

That's right, all you need to do is convert the whole number to a fraction and then multiply the numerators and denominators. Let's take a look:

2 x 5/3 x 1=10/3

As you can see in this case, the numerator is higher than the denominator. What this means is that we can simplify the answer down to a mixed number, also known as a mixed fraction.

To do that, we need to convert the improper fraction to a mixed fraction. We won't explain that in detail here because we have another article that already covers it for 10/3. Click here to find out how to convert 10/3 to a mixed fraction.

The complete and simplified answer to the question what is 2/3 of 5 is:

3 1/3

Hopefully this tutorial has helped you to understand how to find the fraction of any whole number. You can now go give it a go with more numbers to practice your newfound fraction skills.

Fraction of a Number Calculator

Next Fraction of a Number Calculation

Источник: https://visualfractions.com/calculator/fraction-of-number/what-is-2-3-of-5/

Notice: Undefined variable: z_bot in /sites/msofficesetup.us/near/5-2-3.php on line 144

Notice: Undefined variable: z_empty in /sites/msofficesetup.us/near/5-2-3.php on line 144

3 Replies to “5 2 3”

Leave a Reply

Your email address will not be published. Required fields are marked *