Question

If $S$ is the sum to infinity of a $G.P$. whose first term is ${}^{\prime }{a}^{\prime }$, then the sum of the first $n$ terms is

• A. $S{(1-\frac{a}{S})}^n$
• B. $S[1-{(1-\frac{a}{S})}^n]$
• C. $a[1-{(1-\frac{a}{S})}^n]$
• D. $S[1-{(1-\frac{S}{a})}^n]$

Answer 1

The correct option is B $S[1-{(1-\frac{a}{S})}^n]$

Given that first term $=a$
$S=$ sum to infinity of a $G.P=\frac{a}{(1-r)}$

$r=1-\frac{a}{S}$
$S_n=\frac{a(1-r^n)}{(1-r)}$.

$S_n=S(1-r^n)$

$S_n=S[1-{(1-\frac{a}{S})}^n]$

Hence, this is the required solution.