Question

Find three consecutive terms in a G.P. such that the sum of the first two terms is $9$ and the product of all the three terms is $216$.

Answer 1

Let the terms of G.P be $\frac{a}{r},a,ar$
Then $\frac{a}{r}+a=\mathrm{9........}\left(i\right)$
Substituting this value of $a=6$ in equation $\left(i\right)$, we have
$\frac{6}{r}+6=9$
$\therefore$ $6+6r=9r$
$\therefore$ $9r-6r=6$
$\therefore$ $3r=6$
$\therefore$ $r=\frac{6}{3}$
$=2$
$\therefore 1^{st}$ term $\frac{a}{r}=\frac{6}{2}=3$
$\therefore 2^{nd}$ term $a=6$
$\therefore 3^{rd}$ term $ar=6\times 2=12$
Thus the three terms in a G.P are $3,6,12$.