Question

The first two terms of an infinite G.P. are together equal to $5$, and every term is $3$ times the sum of all the terms that follow it' find the series.

Answer 1

$a=$ first term & $r=$ common ratio of G.P.
Given : $a+ar=5$
$a{r}^2=\frac{3a{r}^3}{1-r}$
$\Rightarrow 1-r=3r$
$\Rightarrow r=\frac{1}{4}$
$a=\frac{5}{1+\frac{1}{4}}=4$
So, the series is $4,1,\frac{1}{4},\frac{1}{16}$ . . . . . . . . . . . .