Question

The sum of the first 15 multiples of 8 is
(a) 920
(b) 860
(c) 900
(d) 960​

Answer 1

$\huge\boxed{\fcolorbox{black}{pink}{AnSweR:}}$

960

Hint : First write the first few multiples of 8. We observe that they are in A.P. Find the first term and common difference of this A.P. Then find the sum of first 15 terms of this A.P. using the formula

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

$\huge\boxed{\fcolorbox{black}{pink}{ Explanation :}}$

In this question, we need to find the sum of the first 15 multiples of 8.

The first few multiples of 8 are 8, 16, 24, 32, …

We can observe that these multiples are in an A.P.

The first term of this A.P. is a = 8.

Let us find the common difference of this A.P.

The common difference, d = 16 – 8 = 24 – 16 = 8

Hence, for this A.P., a = 8 and d = 8.

We need to find the sum of the first fifteen terms of this A.P.

i.e. we need to find S15, where Sn denotes the sum of the first n terms of an A.P.

We know that the general formula to calculate the sum of the first n terms of an A.P. i.e. Sn is the product of half of the number of terms and the sum of twice of the first term to the product of the common difference and the number of terms minus one.

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

Substituting a = 8, d = 8, and n = 15 in the above equation, we will get the following:

S15 = 15/2 [2 × 8 ( 15-1 )8]

S15 = 15/2 [16+14×8]

S15 = 15 × 128/2 = 960

So, the sum of the first 15 multiples of 8 is equal to 960.