Question

If product of three consecutive terms of a G.P. is $216$ and sum of their products taken in pairs is $156,$ then the sum of these three terms is

Answer 1

Let the three consecutive terms be $\frac{a}{r},a,ar.$
Then, product $=216$
$\Rightarrow \frac{a}{r}\times a\times ar=216$
$\Rightarrow a^3=216\Rightarrow a=6$
And $\frac{a}{r}\times a+a\times ar+ar\times \frac{a}{r}=156$
$\Rightarrow \frac{a^2}{r}+a^{2}r+a^2=156$
$\Rightarrow \frac{a}{r}+ar+a=26$
Hence, the sum of these three terms is $26.$