Question

If the sum to $2n$ terms of the $A.P.2,5,8,11,...$ is equal to the sum to $n$ terms of the $57,59,61,63,...,$ then $n$ =

• A. $10$
• B. $11$
• C. $12$
• D. $13$

Answer 1

Answer: (B)

Let sum of 2n terms of the $AP57,59,61,63$
is $S_n$ .
$\therefore$ $S_n=\frac{n}{2}[2\times 57+(n-1)2]$
$\frac{n}{2}(2n+112)$
According to question $S_{2n}=S_n$
$\Rightarrow$ $n(6n+1)=\frac{n}{2}(2n+112)$
$\Rightarrow$ $12n+2=2n+112$
$\Rightarrow$ $10n=110$
$\Rightarrow$ $n=11$