# Find the sum of the first 15 multiples of 8.

By Ritesh|Updated : August 5th, 2022

The sum of the first 15 multiples of 8 is 960. The first 8 multiples of 8 are 8, 16, 24, 32, 40, 48, 56,64.......120. These are in an A.P. with an 8 for the first term and an 8 for the common difference.

Therefore, a = 8

d = 8

S15 = ?

We know that:

Sn = n/2 [2a + (n - 1)d]

Substituting the values in the above formula we get:

S15 = 15/2 [2 (8) + (15 - 1) 8]

On simplification:

S15 = 7.5 [16 + (14) 8]

S15 = 7.5 [16 + 112]

S15 = 7.5 

Simplifying the above equation we get:

S15 = 960

### Arithmetic Progression

It is known as the AP sequence because it always has a consistent difference between two consecutive phrases.

Notation in AP:

The following are some of the key terms we will encounter in AP:

• First term (a)
• nth Term (an)
• Common difference (d)
• Sum of the first n terms (Sn)

First term of AP:

The AP can alternatively be expressed using the following popular distinctions;

a, a + d, a + 2d, a + 3d, a + 4d, ……….,a + (n – 1) d

where “a” is the first term of the progression.

Formulas of AP:

When we study Arithmetic Progression, which is associated with: There are two key formulas we encounter:

• The nth term of AP

an = a + (n − 1) × d

Where,

a = First term

d = Common difference

n = number of terms

an = nth term

• Sum of the first n terms

If the first term, common difference, and total terms are known, it is possible to determine the sum of the first n terms for an AP. Below is a description of the arithmetic progression sum's formula:

Consider an AP consisting “n” terms.

Sn = n/2[2a + (n − 1) × d]

The AP sum formula is used to get the total of n terms in a series.

Summary:

## Find the sum of the first 15 multiples of 8.

960 is the sum of the first 15 multiples of 8. For an AP, the sum of the first n terms can be calculated if the first term, common difference, and total terms are known. The formula for the arithmetic progression sum is given by the formula Sn = n/2 [2a + (n - 1)d]. GradeStack Learning Pvt. Ltd.Windsor IT Park, Tower - A, 2nd Floor, Sector 125, Noida, Uttar Pradesh 201303 bepstudentsupport@byjus.com