Question

If the sum of the first $2n$ terms of $2,5,8,....$ is equal to the sum of the first $n$ terms of $57,59,61,....$, then $n$ is equal to

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

Answer 1

The correct option is C $11$

In the series $2,5,8,....$ first term is $2$ and common difference is $3$.

Also, in the series $57,59,61,....$ first term is $57$ and common difference is $2$.

Sum of the first $2n$ terms of $2,5,8,....$ is equal to the sum of the first $n$ terms of $57,59,61,....$

Therefore, $\frac{2n}{2}\{2.2+(2n-1\left)3\right\}=\frac{n}{2}\{2\times 57+(n-1\left)2\right\}$
$\Rightarrow 10n=110$
$\Rightarrow$ $n=11$