The sum of the arithmetic sequence 3, 9, 15, if there are 22 terms is **1452**.

Contents

- 1 What is the sum of the arithmetic sequence 3 9 15 if there are 26 terms?
- 2 What is the sum of the arithmetic sequence 3 9 15 if there are 24 terms?
- 3 What is the sum of an arithmetic sequence 3 9 15 if there are 36 terms?
- 4 What is the sum of the arithmetic sequence 3 9 15 if there are 34 terms?
- 5 What is the sum of the geometric sequence 1 3 9 if there are 12 terms?
- 6 What is the sum of the geometric sequence 1 3 9 if there are 11 terms?
- 7 What is the sum of the geometric sequence 1 3 9 if there are 14 terms?
- 8 What is the sum of the arithmetic sequence 3 9 15 51?
- 9 What is finite sequence?
- 10 What is the term in finding the sum of the nth term a geometric sequence?
- 11 What is the sum of the arithmetic sequence 3, 9, 15…, if there are 22 terms?
- 12 Introduction to Arithmetic Progressions
- 13 What Is The Sum Of The Arithmetic Sequence 3, 9, 15., If There Are 22 Terms
- 14 Frequently Asked Question:
- 14.1 What is the sum of the geometric sequence 1 3 9 if there are 13 terms?
- 14.2 What is the sum of the geometric sequence 1 3 9 if there are 14 terms?
- 14.3 What is the sum of the arithmetic sequence 3 9 15 if there are 26 terms?
- 14.4 How do you find the sum of an arithmetic sequence?
- 14.5 What is the sum of the terms in a sequence?
- 14.6 What is the sum of the arithmetic sequence 3 9 15 if there are 24 terms?
- 14.7 What is the sum of the first 26 terms of the arithmetic series?
- 14.8 How do you find the sum of the terms in an arithmetic sequence?
- 14.9 What is the sum of the arithmetic sequence 3 9 15 if there are 26 terms?
- 14.10 What is the sum of the geometric sequence 1 3 9 if there are 12 terms?
- 14.11 How do you find the sum of the terms in an arithmetic sequence?
- 14.12 How do you find the sum of an arithmetic sequence?
- 14.13 What is the sum of the terms in a sequence?

- 15 What Is The Sum Of The Arithmetic Sequence 3, 9, 15., If There Are 24 Terms?
- 16 Frequently Asked Question:
- 16.1 What is the sum of the geometric sequence 1 3 9 if there are 14 terms?
- 16.2 What is the sum of the geometric sequence 1 3 9 if there are 13 terms?
- 16.3 What is the sum of the geometric sequence 1 3 9 if there are 12 terms?
- 16.4 What is the sum of the terms in a sequence?
- 16.5 How can you find the sum of the terms of the arithmetic sequence if the number of terms is unknown?
- 16.6 How do you find the sum of an arithmetic sequence?
- 16.7 What is the sum of the arithmetic sequence 3 9 15 if there are 24 terms?
- 16.8 What is the sum of the first 26 terms of the arithmetic series?
- 16.9 What is the sum of the arithmetic sequence 3 9 15 if there are 24 terms?
- 16.10 What is the sum of an arithmetic sequence?
- 16.11 How do you find the sum of arithmetic equations?
- 16.12 What is the formula for the sum of an arithmetic series?

- 17 what is the sum of the geometric sequence 1, 3, 9, … if there are 10 terms?
- 18 What is the sum of the geometric sequence − 3 18 − 108 if there are 7 terms 5 points?
- 19 What is the sum of the geometric sequence if there are 8 terms?
- 20 What is the sum of the geometric sequence Brainly?
- 21 What is the sum of the geometric sequence if there are seven terms?
- 22 What is the common ratio of the sequence?- 2 6 54?
- 23 What is the sum of the geometric sequence − 4 24 − 144 if there are 6 terms 5 points?
- 24 What are the value of a1 and R of the geometric series?
- 25 What is the sum of the infinite geometric series?
- 26 How many terms are there in the GP 3 6 12 24 384?
- 27 What is the sum of the arithmetic sequence three 915 if there are 22 terms?
- 28 How do you find the sub 1 of a geometric sequence?
- 29 SUM OF THE FIRST N TERMS OF A GEOMETRIC SEQUENCE
- 30 Arithmetic Sequences and Sums
- 31 Arithmetic Sequence
- 32 Advanced Topic: Summing an Arithmetic Series
- 33 Footnote: Why Does the Formula Work?

## What is the sum of the arithmetic sequence 3 9 15 if there are 26 terms?

Summary: The sum of the arithmetic sequence 3, 9, 15, if there are 26 terms is 2028.

## What is the sum of the arithmetic sequence 3 9 15 if there are 24 terms?

The sum of the arithmetic sequence 3, 9, 15, if there are 24 terms is 1728.

## What is the sum of an arithmetic sequence 3 9 15 if there are 36 terms?

The sum of the arithmetic sequence 3, 9, 15, if there are 36 terms is 3888.

## What is the sum of the arithmetic sequence 3 9 15 if there are 34 terms?

The sum of the arithmetic sequence 3, 9, 15, if there are 34 terms is 3468.

## What is the sum of the geometric sequence 1 3 9 if there are 12 terms?

Summary: The sum of the geometric sequence 1, 3, 9, if there are 12 terms is 265720.

## What is the sum of the geometric sequence 1 3 9 if there are 11 terms?

Summary: The sum of the geometric sequence 1, 3, 9, if there are 11 terms is 88573.

## What is the sum of the geometric sequence 1 3 9 if there are 14 terms?

Summary: The sum of the geometric sequence 1, 3, 9, if there are 14 terms is 2391484.

## What is the sum of the arithmetic sequence 3 9 15 51?

Therefore, the sum upto 22 terms is 1452.

## What is finite sequence?

A sequence is finite if it has a limited number of terms and infinite if it does not. Finite sequence: {4,8,12,16,…, 64} The first of the sequence is 4 and the last term is 64. Since the sequence has a last term, it is a finite sequence.

## What is the term in finding the sum of the nth term a geometric sequence?

For r≠1 r ≠ 1, the sum of the first n terms of a geometric series is given by the formula s=a1−rn1−r s = a 1 − r n 1 − r.

## What is the sum of the arithmetic sequence 3, 9, 15…, if there are 22 terms?

Assuming that there are n initial terms in the sequence and that the difference between the first term and the difference between terms is d, the total of all of the first n terms is provided bya + (a+d) +, and the sum of all of the second terms is given bya+2d, and so on (n-1) d = sum (k=0) is a mathematical expression. (n-1)(a+kd) = n((a 1+a n)/2)where a i is the ith term in the series (so a 1 = a and a n = a + (n-1)d) and n is the number of terms in the sequence. (The derivation of this formula is provided further below.) Applying the method here with a = 3 and d = 6 results in the following: The sum of three nines and fifteens is plus.

In the following, we will show how to derive the arithmetic sum formula, which is not necessarily essential in order to solve the previously stated issue.

## Introduction to Arithmetic Progressions

Generally speaking, a progression is a sequence or series of numbers in which the numbers are organized in a certain order so that the relationship between the succeeding terms of a series or sequence remains constant. It is feasible to find the n thterm of a series by following a set of steps. There are three different types of progressions in mathematics:

- Arithmetic Progression (AP), Geometric Progression (GP), and Harmonic Progression (HP) are all types of progression.

AP, also known as Arithmetic Sequence, is a sequence or series of integers in which the common difference between two subsequent numbers in the series is always the same. As an illustration: Series 1: 1, 3, 5, 7, 9, and 11. Every pair of successive integers in this sequence has a common difference of 2, which is always true. Series 2: numbers 28, 25, 22, 19, 16, 13,. There is no common difference between any two successive numbers in this series; instead, there is a strict -3 between any two consecutive numbers.

### Terminology and Representation

- Common difference, d = a 2– a 1= a 3– a 2=. = a n– a n – 1
- A n= n thterm of Arithmetic Progression
- S n= Sum of first n elements in the series
- A n= n

### General Form of an AP

Given that ais treated as a first term anddis treated as a common difference, the N thterm of the AP may be calculated using the following formula: As a result, using the above-mentioned procedure to compute the n terms of an AP, the general form of the AP is as follows: Example: The 35th term in the sequence 5, 11, 17, 23,. is to be found.

Solution: When looking at the given series,a = 5, d = a 2– a 1= 11 – 5 = 6, and n = 35 are the values. As a result, we must use the following equations to figure out the 35th term: n= a + (n – 1)da n= 5 + (35 – 1) x 6a n= 5 + 34 x 6a n= 209 As a result, the number 209 represents the 35th term.

### Sum of n Terms of Arithmetic Progression

The arithmetic progression sum is calculated using the formula S n= (n/2)

### Derivation of the Formula

Allowing ‘l’ to signify the n thterm of the series and S n to represent the sun of the first n terms of the series a, (a+d), (a+2d),., a+(n-1)d S n = a 1 plus a 2 plus a 3 plus .a n-1 plus a n S n= a + (a + d) + (a + 2d) +. + (l – 2d) + (l – d) + l. + (l – 2d) + (l – d) + l. + (l – 2d) + (l – d) + l. (1) When we write the series in reverse order, we obtain S n= l + (l – d) + (l – 2d) +. + (a + 2d) + (a + d) + a + d + a + d + a + d + a + d + a + d + a + d + a + d + a + d + a + d + a + d + a … (2) Adding equations (1) and (2) results in equation (2).

+ (a + l) + (a + l) + (a + l) +.

(3) As a result, the formula for calculating the sum of a series is S n= (n/2)(a + l), where an is the first term of the series, l is the last term of the series, and n is the number of terms in the series.

d S n= (n/2)(a + a + (n – 1)d)(a + a + (n – 1)d) S n= (n/2)(2a + (n – 1) x d)(n/2)(2a + (n – 1) x d) Observation: The successive terms in an Arithmetic Progression can alternatively be written as a-3d, a-2d, a-d, a, a+d, a+2d, a+3d, and so on.

### Sample Problems on Arithmetic Progressions

Problem 1: Calculate the sum of the first 35 terms in the sequence 5,11,17,23, and so on. a = 5 in the given series, d = a 2–a in the provided series, and so on. The number 1 equals 11 – 5 = 6, and the number n equals 35. S n= (n/2)(2a + (n – 1) x d)(n/2)(2a + (n – 1) x d) S n= (35/2)(2 x 5 + (35 – 1) x 6)(35/2)(2 x 5 + (35 – 1) x 6) S n= (35/2)(10 + 34 x 6) n= (35/2)(10 + 34 x 6) n= (35/2)(10 + 34 x 6) S n= (35/2)(10 + 204) S n= (35/2)(10 + 204) S n= (35/2)(10 + 204) S n= (35/2)(10 + 204) S n= (35/2)(10 + 204) A = 35214/2A = 3745S n= 35214/2A = 3745 Find the sum of a series where the first term of the series is 5 and the last term of the series is 209, and the number of terms in the series is 35, as shown in Problem 2.

Problem 2.

S n= (35/2)(5 + 209) S n= (35/2)(5 + 209) S n= (35/2)(5 + 209) A = 35214/2A = 3745S n= 35214/2A = 3745 Problem 3: A amount of 21 rupees is divided among three brothers, with each of the three pieces of money being in the AP and the sum of their squares being the sum of their squares being 155.

Solution: Assume that the three components of money are (a-d), a, and (a+d), and that the total amount allocated is in AP.

155 divided by two equals 155 Taking the value of ‘a’ into consideration, we obtain 3(7) 2+ 2d.

2= 4d = 2 = 2 The three portions of the money that was dispersed are as follows:a + d = 7 + 2 = 9a = 7a – d = 7 – 2 = 5a = 7a – d = 7 – 2 = 5a = 7a – d = 7 – 2 = 5a = 7a – d = 7 – 2 = 5a = 7a – d = 7 – 2 = 5a = 7a – d = 7 – 2 = 5 As a result, the most significant portion is Rupees 9 million.

## What Is The Sum Of The Arithmetic Sequence 3, 9, 15., If There Are 22 Terms

If there are 24 terms in the arithmetic sequence 3 9 15, what is the sum of the series? The following is the formula for the sum of an arithmetic sequence: Substitute: The answer is 1728. Furthermore, if there are 26 terms and 5 points in the arithmetic series 3 9 15, what is the sum of the sequence? , The sum of anarithmetic series is: S = n*(a 1+a n)/2, which is straightforward. In your example, n is the number of words, which is 26. The value of a n is a 26. And last, how do you compute the sum of the terms in an arithmetic sequence?

Multiply the average by the number of terms in the series to get the final result.

As a result, the total of the numbers 10, 15, 20, 25, and 30 equals 100.

## Frequently Asked Question:

It is 265,720 to add up all of the numbers in the geometric series 1,3,9. using 12 terms.

### What is the sum of the geometric sequence 1 3 9 if there are 13 terms?

1, 3, 9,. In addition, the total number of theterms is n =13. So the total of the provided geometric series is 797161 in the given case.

### What is the sum of the geometric sequence 1 3 9 if there are 14 terms?

Answer: The sum of the geometric sequences 1, 3, 9,., up to and including 14 terms is 1 /2 /2 /2

### What is the sum of the arithmetic sequence 3 9 15 if there are 26 terms?

The sum of anarithmetic series is: S = n*(a 1+a n)/2, which is straightforward. In your example, n is the number of words, which is 26. The value of a n is a 26.

### How do you find the sum of an arithmetic sequence?

Calculating the sum of an arithmetic series is accomplished by multiplying the number of terms by the average of the first and final terms. For example, the sum of 3 + 7 + 11 + 15 + 99 has a 1 = 3 and a d = 4. Make advantage of the explicitformulafor anarithmetic sequence to locaten.

### What is the sum of the terms in a sequence?

Aseries are the total of all the terms in a sequence of events.

### What is the sum of the arithmetic sequence 3 9 15 if there are 24 terms?

The following is the formula for the sum of an arithmetic sequence: Answer: 1,728. Substitute: 1,728.

### What is the sum of the first 26 terms of the arithmetic series?

The 26th term will be 7+4(26 -1)=7+100=107, which is a multiple of 7. As a result, the total of theseries will be (107+7)*13=1482.

### How do you find the sum of the terms in an arithmetic sequence?

To achieve this, add the two integers together and divide the result by two. Multiply the average by the number of terms in the series to get the final result. The sum of the arithmetic sequence will be returned as a result of this. As a result, the total of the numbers 10, 15, 20, 25, and 30 equals 100.

### What is the sum of the arithmetic sequence 3 9 15 if there are 26 terms?

The sum of anarithmetic series is: S = n*(a 1+a n)/2, which is straightforward. In your example, n is the number of words, which is 26. The value of a n is a 26.

### What is the sum of the geometric sequence 1 3 9 if there are 12 terms?

It is 265,720 to add up all of the numbers in the geometric series 1,3,9. using 12 terms.

### How do you find the sum of the terms in an arithmetic sequence?

To achieve this, add the two integers together and divide the result by two. Multiply the average by the number of terms in the series to get the final result. The sum of the arithmetic sequence will be returned as a result of this. As a result, the total of the numbers 10, 15, 20, 25, and 30 equals 100.

### How do you find the sum of an arithmetic sequence?

Calculating the sum of an arithmetic series is accomplished by multiplying the number of terms by the average of the first and final terms.

For example, the sum of 3 + 7 + 11 + 15 + 99 has a 1 = 3 and a d = 4. Make advantage of the explicitformulafor anarithmetic sequence to locaten.

### What is the sum of the terms in a sequence?

Aseries are the total of all the terms in a sequence of events. (It has been visited 1 time, with 1 visit today)

## What Is The Sum Of The Arithmetic Sequence 3, 9, 15., If There Are 24 Terms?

The following is the formula for the sum of an arithmetic sequence: Substitute: The answer is 1728. The date is May 15, 2018. In the arithmetic sequence 3 9 15, what is the sum of the digits? The total of all of this is 3888. Furthermore, if there are 26 terms and 5 points in the arithmetic series 3 9 15, what is the sum of the sequence? , The sum of anarithmetic series is: S = n*(a 1+a n)/2, which is straightforward. In your example, n is the number of words, which is 26. The value of a n is a 26.

To achieve this, add the two integers together and divide the result by two.

The sum of the arithmetic sequence will be returned as a result of this.

## Frequently Asked Question:

Answer: The sum of the geometric sequences 1, 3, 9,., up to and including 14 terms is 1 /2 /2 /2

### What is the sum of the geometric sequence 1 3 9 if there are 14 terms?

To find out, add up the terms in the geometric sequence 1, 3, 9,., up to 14 and divide by 2.

### What is the sum of the geometric sequence 1 3 9 if there are 13 terms?

1, 3, 9,. In addition, the total number of theterms is n =13. So the total of the provided geometric series is 797161 in the given case.

### What is the sum of the geometric sequence 1 3 9 if there are 12 terms?

It is 265,720 to add up all of the numbers in the geometric series 1,3,9. using 12 terms.

### What is the sum of the terms in a sequence?

Aseries are the total of all the terms in a sequence of events.

### How can you find the sum of the terms of the arithmetic sequence if the number of terms is unknown?

We can calculate the sum of the terms in the arithmetic sequence by discovering the unknown numbers of terms (n) and using the nth formula of the arithmetic sequencean=a1+(n-1)d, and we can also find the common difference (d) if necessary. We can also find the common difference (d) if necessary.

### How do you find the sum of an arithmetic sequence?

It is possible to calculate the total of anarithmetic series by multiplying the number of terms by the average of the first and final terms. For example, the sum of 3 + 7 + 11 + 15 + 99 has a 1 = 3 and a d = 4. Make use of the explicit formula for anarithmetic sequence to locate n.

### What is the sum of the arithmetic sequence 3 9 15 if there are 24 terms?

The following is the formula for the sum of an arithmetic sequence: Answer: 1,728. Substitute: 1,728.

### What is the sum of the first 26 terms of the arithmetic series?

The 26th term will be 7+4(26 -1)=7+100=107, which is a multiple of 7. As a result, the total of theseries will be (107+7)*13=1482.

### What is the sum of the arithmetic sequence 3 9 15 if there are 24 terms?

The following is the formula for the sum of an arithmetic sequence: Answer: 1,728. Substitute: 1,728.

### What is the sum of an arithmetic sequence?

Calculating the sum of an arithmetic series is accomplished by multiplying the number of terms by the average of the first and final terms. … Use the explicit formula for anarithmetic sequence to obtain the value of n. We solve 3 + (n – 1)4 = 99 to get n = 25 as a result of the previous equation.

### How do you find the sum of arithmetic equations?

To achieve this, add the two integers together and divide the result by two.

Multiply the average by the number of terms in the series to arrive at the final answer. This will provide you with the sum of the arithmetics series. As a result, the total of the numbers 10, 15, 20, 25, and 30 equals 100.

### What is the formula for the sum of an arithmetic series?

When n words in anarithmetic sequence are added together, the result is (n/2)(a1+an). The formula for thearithmetic series is referred to as thearithmetic series formula. (It has been visited 1 time, with 1 visit today)

## what is the sum of the geometric sequence 1, 3, 9, … if there are 10 terms?

The formula for finding the sum of the first n terms of a geometric series isa times 1 minus r to the nth power over 1 minus rwhere n is the number of terms for which we are looking for the sum, an is the first term of our sequence, and r is our common ratio of the terms in our sequence. A geometric series is the sum of the terms of a geometric sequence. A geometric sequence is the sum of the terms of a geometric series. This is a geometric sequence since there is a common ratio between each of the terms in the series.

a11r is an infinite geometric series with |r|

In the general purpose formula, the sum is S=arn1r1.

The total of a GP is determined by the number of phrases in the GP.

## What is the sum of the geometric sequence − 3 18 − 108 if there are 7 terms 5 points?

In this case, the total of the 7 terms in the G.P. Series is 119973, which is a positive integer. I hope that is of assistance.

## What is the sum of the geometric sequence if there are 8 terms?

If there are 8 terms in the geometric series 4, 16, 64,., the sum of the sequence is 87380.

## What is the sum of the geometric sequence Brainly?

Geometric series is the sum of the first n terms of a geometric sequence, and it is composed of the first n terms of the geometric sequence. The following is a step-by-step explanation: A finite geometric series can be represented by the formula Sn=a1(rn)rr1, where n is the number of terms, a1 is the first term, and r is the common ratio of the terms.

## What is the sum of the geometric sequence if there are seven terms?

If there are 7 terms in the geometric series 3, 15, 75,., the total of the sequence is 58593.

## What is the common ratio of the sequence?- 2 6 54?

The common ratio of the numbers in the sequence -2, 6, -18, 54,. is three.

## What is the sum of the geometric sequence − 4 24 − 144 if there are 6 terms 5 points?

If there are 6 terms in the geometric series -4, 24, -144,., the total of the sequence is 26660.

## What are the value of a1 and R of the geometric series?

The values of a1 and r are 2 and -1, respectively, as shown in the diagram. Let’s try to figure out what a1 and r are worth. Explanation: The terms in the geometric series are 2, -2, 2, -2, 2, -2,., and they are as follows:

## What is the sum of the infinite geometric series?

Sequences, both finite and infinite A series is finite if it has a finite number of terms, and it is endless if it contains an unlimited number of terms. Sequence with a finite number of steps: The first term in the series is 4 and the last term is 64, hence the sequence is complete. Because the series contains a final term, it is considered to be a finite sequence.

## How many terms are there in the GP 3 6 12 24 384?

The total number of terms is eight.

## What is the sum of the arithmetic sequence three 915 if there are 22 terms?

Summary: If there are 22 terms in the arithmetic series 3, 9, 15,., the total of the sequence is 1452.

## How do you find the sub 1 of a geometric sequence?

Given that the numbers 3, 9, 27, 81, 243,.

are in geometric progression, the following statement is true: We need to figure out what the next number in the series is. When the following number is used, it denotes the 6th term in the series. As a result, the 729th number in the series is the next in the series.

## SUM OF THE FIRST N TERMS OF A GEOMETRIC SEQUENCE

If there are 26 terms in the arithmetic series 3, 9, 15,., what is the sum of the terms in the sequence? choose the function that corresponds to the graph If there are seven terms in the geometric series 4, 24, 144,., what is the sum of the geometric sequence? the sum of the geometric series -3, 18, -108 is what number? If there are eight terms, then If there are seven terms in the geometric series 3, 18, 108,., what is the sum of the geometric sequence? If there are seven terms in the geometric sequence 24, what is the sum of the series?

If there are 8 terms in the geometric sequence 24, what is the sum of the series?

## Arithmetic Sequences and Sums

A sequence is a collection of items (typically numbers) that are arranged in a specific order. Each number in the sequence is referred to as aterm (or “element” or “member” in certain cases); for additional information, see Sequences and Series.

## Arithmetic Sequence

An Arithmetic Sequence is characterized by the fact that the difference between one term and the next is a constant. In other words, we just increase the value by the same amount each time. endlessly.

### Example:

1, 4, 7, 10, 13, 16, 19, 22, and 25 are the numbers 1 through 25. Each number in this series has a three-digit gap between them. Each time the pattern is repeated, the last number is increased by three, as seen below: As a general rule, we could write an arithmetic series along the lines of

- There are two words: Ais the first term, and dis is the difference between the two terms (sometimes known as the “common difference”).

### Example: (continued)

1, 4, 7, 10, 13, 16, 19, 22, and 25 are the numbers 1 through 25. Has:

- In this equation, A = 1 represents the first term, while d = 3 represents the “common difference” between terms.

And this is what we get:

### Rule

It is possible to define an Arithmetic Sequence as a rule:x n= a + d(n1) (We use “n1” since it is not used in the first term of the sequence).

### Example: Write a rule, and calculate the 9th term, for this Arithmetic Sequence:

3, 8, 13, 18, 23, 28, 33, and 38 are the numbers three, eight, thirteen, and eighteen. Each number in this sequence has a five-point gap between them. The values ofaanddare as follows:

- A = 3 (the first term)
- D = 5 (the “common difference”)
- A = 3 (the first term).

Making use of the Arithmetic Sequencerule, we can see that_xn= a + d(n1)= 3 + 5(n1)= 3 + 3 + 5n 5 = 5n 2 xn= a + d(n1) = 3 + 3 + 3 + 5n n= 3 + 3 + 3 As a result, the ninth term is:x 9= 5 9 2= 43 Is that what you’re saying? Take a look for yourself! Arithmetic Sequences (also known as Arithmetic Progressions (A.P.’s)) are a type of arithmetic progression.

## Advanced Topic: Summing an Arithmetic Series

To summarize the terms of this arithmetic sequence:a + (a+d) + (a+2d) + (a+3d) + (a+4d) + (a+5d) + (a+6d) + (a+7d) + (a+8d) + (a+9d) + (a+9d) + (a+9d) + (a+9d) + (a+9d) + (a+9d) + ( make use of the following formula: What exactly is that amusing symbol? It is referred to as The Sigma Notation is a type of notation that is used to represent a sigma function. Additionally, the starting and finishing values are displayed below and above it: “Sum upnwherengoes from 1 to 4,” the text states. 10 is the correct answer.

### Example: Add up the first 10 terms of the arithmetic sequence:

The values ofa,dandnare as follows:

- In this equation, A = 1 represents the first term, d = 3 represents the “common difference” between terms, and n = 10 represents the number of terms to add up.

As a result, the equation becomes:= 5(2+93) = 5(29) = 145 Check it out yourself: why don’t you sum up all of the phrases and see whether it comes out to 145?

## Footnote: Why Does the Formula Work?

Let’s take a look at why the formula works, since we get to apply an intriguing “trick” that’s worth knowing.First, we’ll refer to the entire sum as “S,” which will be written as S = a + (a + d) +. Next, rewrite S in reverse order: S = (a + (n1)d)+ (a + (n2)d) Next, rewrite S in reverse order: S = (a + (n1)d)+(a + (n2)d) +(a + d)+aNow, word by term, add those two together:

S | = | a | + | (a+d) | + | . | + | (a + (n-2)d) | + | (a + (n-1)d) |

S | = | (a + (n-1)d) | + | (a + (n-2)d) | + | . | + | (a + d) | + | a |

2S | = | (2a + (n-1)d) | + | (2a + (n-1)d) | + | . | + | (2a + (n-1)d) | + | (2a + (n-1)d) |

Each and every term is the same! Furthermore, there are “n” of them. 2S = n (2a + (n1)d) = n (2a + (n1)d) Now, we can simply divide by two to obtain the following result: The function S = (n/2) (2a + (n1)d) is defined as This is the formula we’ve come up with: