Question

Let $S_n$ denotes the sum of first $n$ terms of an A.P . If $S_{3n}=5S_n$, then $S_{2n}:S_n$.

• A. $8:3$
• B. $3:8$
• C. $6:1$
• D. $2:3$

Answer 1

The correct option is A $8:3$

$\frac{S_{3n}}{S_n}=5$

$⟹5=\frac{\left(3n/2\right)[2a+(3n-1\left)d\right]}{\left(n/2\right[2a+(n-1)d\left]\right)}$

$⟹10a+(5n-5d)=6a+(9n-3)d$

$⟹2a=(2n+1)d$

So, $\frac{S_{2n}}{S_n}=$$\frac{\left(2n/2\right)[2a+(2n-1\left)d\right]}{\left(n/2\right[2a+(n-1)d\left]\right)}$

$⟹\frac{S_{2n}}{S_n}=\frac{2\times 4n}{3n}=\frac{8}{3}$