Question

Firs term of an arithmetic progression is $2$. If the sum of its first five terms is equal to one-fourth of the sum of the next five terms, then the sum of its first $30$ terms is

• A. $2670$
• B. $2610$
• C. $-2520$
• D. $2550$

Answer 1

Answer: (D)

$2550$

Given,

First term $a=2$

According to the problem, first 10 are

$a,a+d,a+2d,a+3d,a+4d,a+5d,a+6d,a+7d,a+8d,a+9d$

$5a+10d=\frac{1}{4}(5a+35d)$

$20a+40d=5a+35d$

$15a=-5d$

$3a=-d$

As $a=2$

$d=-6$ and $n=30$

$S_{30}=\frac{n}{2}\left[2\right(a)+(n-1\left)d\right]$

$S_{30}=\frac{30}{2}\left[2\right(2)+(29\left)\right(-6\left)\right]$

$=-2550$