Question

If sum of 3 terms of a G.P is S, product is P, and sum of reciprocal of its terms is R, then the value of $P^2{R}^3$ equal to

• A. $S$
• B. $S^3$
• C. $2S^2$
• D. $S^2/5$

Answer 1

The correct option is B $S^3$

Let $\frac{a}{r},a,ar$ be the three terms of G.P

$S=\frac{a}{r}+a+arp=\left(\frac{a}{r}\right)\left(a\right)\left(ar\right)=a^{3}R=\frac{r}{a}+\frac{1}{a}+\frac{1}{ar}{P}^2{R}^3=a^6.\frac{1}{a^3}(r^3+1+\frac{1}{r^3}+3(r+1\left)\right(1+\frac{1}{r}\left)\right(r+\frac{1}{r})=a^3(r+1+\frac{1}{r}{)}^3=(ar+a+\frac{a}{r}{)}^3{P}^2{R}^3=S^3$