Question

Let $S_n$ denote the sum of $n$ terms of an AP, if $S_{2n}=3S_{n,}$ then the ratio $\frac{S_{3n}}{S_n}$ is equal to

• A. 9
• B. 6
• C. 16
• D. 12

Answer 1

Answer: (B)

6

Solution :-

we know $S_n=\frac{n(n+1)}{2}$

Given $S_{2n}=3s_n$

$\Rightarrow \frac{2n(2n+1)}{2}=\frac{3.n(n+1)}{2}$

$\Rightarrow 4n+2=3n+3$

$\Rightarrow n=1$

then $\frac{S_{3n}}{S_n}=\frac{3n(3n+1)}{2}÷\frac{n(n+1)}{2}=\frac{3\times 4}{2\times 1}=6$