Question

If $S,P$ and $R$ are the sum, product and sum of the reciprocals of $n$ terms of an increasing $G.P$ respectively and $S^n=R^n.P^k$, then $k$ is equal to

• A. $1$
• B. $2$
• C. $3$
• D. None of these

Answer 1

Answer: (B)

$S=\frac{a\left(1-r^n\right)}{1-r},P=a^n.r^{\frac{n\left(n-1\right)}{2}}$
$R=\frac{1}{a}+\frac{1}{ar}+\frac{1}{a{r}^2}+.....nterms=\frac{1-r^n}{a\left(1-r\right)r^{n-1}}$
$S^n=R^n{P}^k\Rightarrow {\left(\frac{S}{R}\right)}^n=P^k$
$\Rightarrow {\left(a^2{r}^{n-1}\right)}^n=P^k<br/>\Rightarrow P^2=P^k\Rightarrow k=2$