Question

The sum of first two terms of an infinite $G.P$ is $5$ and each term is three times the sum of succeeding terms. Find the series.

Answer 1

Here $a+ar=5$
$T_p=3(T_{p+1}+T_{p+2}+...\infty )$
$\therefore {ar}^{p-1}=3.\frac{{ar}^p}{1-r}$
$\therefore 1-r=3r$
or $r=\frac{1}{4}$ hence $a=4$, etc.