Question

The first term of a GP is 1. The sum of the third and fifth term is 90. Find the common ratio of GP.

Answer 1

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

$a=1$

$a_3=a{r}^2=r^2$

$a_5=a{r}^4=r^4$

$r^2+r^4=90$

$r^4+r^2-90=0$

We have a formula for solving quadratic equation $a{x}^2+bx+c=0$ is

$x=\frac{-b\pm \sqrt{b^2-4ac}}{2a}$

$\therefore r^2=\frac{-1\pm 19}{2}=-10or9$

Therefore, $r=\pm 3$.

Thus, the common ratio of the GP is $\pm 3$.