Question

The first terms of a G.P. is $1$. The sum of the third and fifth term is $90$. Find the common ratio.

Answer 1

$a=1$ $a,ar,a{r}^2,a{r}^3,a{r}^4$

$a{r}^2+a{r}^4=90$

$a(r^2+r^4)=90$

$r^2(1+r^2)=90$

$r^2=90$ $1+r^2=90$

$r=\pm \sqrt{9}0$ $r=\pm \sqrt{8}9$