Find the sum of the first 15 multiples of 7

Madan Mohan

Question: Find the sum of the first 15 multiples of 7

The sum of the first n terms of an AP is given by Sₙ = n/2 [2a + (n - 1) d] or or Sₙ = n/2 [a + l].

Here, a is the first term,

d is a common difference and

n is the number of terms.

The multiples of 7 are 7, 14, 21, 38, 35, 42, 49, 56, 63, 70, 77, 84....

These numbers are in an A.P.

As we need to find the sum of the first 15 multiples of 7.

Hence,

First-term, a = 7

Common difference, d = 7

Number of terms, n = 15

As we know the sum of n terms is given by the formula Sₙ = n/2 [2a + (n - 1) d]

S₁₅ = 15/2 [2 × 7 + (15 - 1)7]

= 15/2 [14 + 14 × 7]

= 15/2 [14 + 98]

= 15/2 × 112

= 15 × 56 = 840

Thus, the sum of first 15 multiples of 7 are 840.