Question

If the sum of the first 2n terms of the 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

Answer: (C)

$2,5,8,\dots \dots .....A.P.$
$S_{2n}=n[4+(2n-1)3]$
$S_{2n}=n[6n+1]$
$57,59,61,\dots \dots ....$
$S_n=\frac{n}{2}[2\times 57+(n-1)\times 2]$
$S_n=n[57+n-1]=n[n+56]$
$S_n=S_{2n}$
$n(n+56)=n(6n+1)$
$n\ne 0\therefore n+56=6n+1$
$5n=55$
$\therefore n=11$