Question

If the sum of first 2n terms of A.P . 2, 5, 8,... is equal to the sum of the first n terms of the A.P . 57, 59, 61, ....., then n equals-

• A. 10
• B. 12
• C. 11
• D. 13

Answer 1

The correct option is C 11

The sum of first $2n$ terms of $2,5,8,...$ is
$=\frac{2n}{2}\left[2\right(2)+(2n-1\left)\right(3\left)\right]$
$=n(6n+1)$
The sum of $n$ terms of $57,59,61,...$ is
$=\frac{n}{2}\left[2\right(57)+(n-1\left)\right(2\left)\right]$
$=n(56+n)$
Also, $n(6n+1)=n(56+n)$
$\Rightarrow 6n+1=56+n$
$\Rightarrow 5n=55$
$\Rightarrow n=11$