Question

In a geometric progression, $S_{2n}÷S_n$ is equal to

• A. $\frac{r^n+1}{r^n-1}$
• B. $r^n+1$
• C. $r^{n+1}$
• D. $r^n-1$

Answer 1

The correct option is B $r^n+1$

Formula for sum of $n$ terms in geometric progression is given by

$S_n=\frac{a(1-r^n)}{1-r}$, where $a$ is the first term and $r$ is the common ratio, $r\ne 1$

$\therefore$ $S_{2n}÷S_n=\frac{\frac{a(1-r^{2n})}{(1-r)}}{\frac{a(1-r^n)}{(1-r)}}$

$=\frac{(1^2-(r^n{)}^2)}{(1-r^n)}$

$=\frac{(1-r^n)(1+r^n)}{(1-r^n)}$

$=(1+r^n)$

Hence, the answer is B.