Question

The sum of an infinite GP is 8, its second term is 2, find its first term.

Answer 1

Let a be the first term and r the common ratio of the GP.

Given, $S_{\infty }=8$ and $ar=2$

$\frac{a}{1-r}=8$ and $r=\frac{2}{a}$

$\frac{a}{1-\left(2/a\right)}=8$

$a^2-8a+16=0$

$(a-4{)}^2=0$

$a=4$