Question

Sn denotes the sum of first $n$ terms of the A.P. $1,2,3,4,......$, then $S_{2n}=3Sn$
$\frac{S_{3n}}{Sn}=?$

Answer 1

Formula,

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

Given,

$S_{2n}=3S_n$

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

$2(2n+1)=3(n+1)$

$4n+2=3n+3$

$\therefore n=1$

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

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

$=\frac{3\times 4}{1\times 2}=6$