Question

Let $S_n$ denote the sum of the first '$n$' terms of an A.P and $S_{2n}=3Sn$. Then the ratio $S_{3n}:S_n$ is equal to

• A. $4:1$
• B. $6:1$
• C. $8:1$
• D. $10:1$

Answer 1

The correct option is B $6:1$

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

Now it is is given that $S_{2n}=3S_n$

$\Rightarrow \frac{2n(2n+1)}{2}=\frac{3n(n+1)}{2}\Rightarrow 2(2n+1)=3(n+1)\Rightarrow 4n+2=3n+3\Rightarrow 4n-3n=3-2\Rightarrow n=1$

Then $\frac{S_{3n}}{S_n}=\frac{3n(3n+1)/2}{n(n+1)/2}=\frac{3\times 4}{1\times 2}=\frac{6}{1}\Rightarrow 6:1$

Option B is the correct answer.