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 first term of the series ?

Answer 1

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