Question

The sum of an infinite G.P. is $\frac{80}{9}$ and its common ratio is $\frac{-4}{5}$. Find its first term.

Answer 1

Formula,

$S_{\infty }=\frac{a}{1-r}$

Given,

$\frac{80}{9}=\frac{a}{1-(-\frac{4}{5})}$

$\frac{80}{9}=\frac{a}{\frac{9}{5}}$

$\therefore a=16$