Find the sum of the first 15 multiples of 8.
By BYJU'S Exam Prep
Updated on: September 25th, 2023
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 [128]
Simplifying the above equation we get:
S15 = 960
Table of content
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].
