Question

Let $S_n$ denotes the sum of first $n$ terms of an $A.P$. If $S_{2n}=3S_n$, then the ratio $S_{3n}/S_n$ is equal to

• A. $4$
• B. $6$
• C. $8$
• D. $10$

Answer 1

The correct option is B $6$

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

$\therefore S_{2n}=\frac{2n(2n+1)}{2}$

Now, $S_{2n}=3S_n\Rightarrow \frac{2n(2n+1)}{2}=3\frac{n(n+1)}{2}$

or, $4x+2=3n+3\Rightarrow n=1$

$\therefore \frac{S_{3n}}{S_n}=\frac{3\left(1\right)\left[3\right(1)+1]}{2}\times \frac{2}{1(1+1)}=\frac{3\times 4}{2}=6$