Question

If the sum of 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

The correct option is C $11$

$S_{2n}=S_n^{\prime }$

$\therefore \frac{2n}{2}[2\times 2+(2n-1\left)3\right]=\frac{n}{2}[2\times 57+(n-1\left)2\right]$

$\therefore 6n+1=n+56$

$\Rightarrow 5n=55$ or $n=11$

$\Rightarrow \left(c\right)$.