Question

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

• A. $\pm 5$
• B. $\pm 2$
• C. $\pm 3$
• D. $\pm 4$

Answer 1

The correct option is C $\pm 3$

Let $r$ be the common ratio of the G.P. It is given that the first term is $a=1$. Now,
$a_3+a_5=90$
$\Rightarrow a{r}^2+a{r}^4=90$
$\Rightarrow r^2+r^4=90$
$\Rightarrow r^4+r^2-90=0$
$\Rightarrow r^4+10r^2-9r^2-90=0$
$\Rightarrow (r^2+10)(r^2-9)=0$
$\Rightarrow r^2-9=0$
$\Rightarrow r=\pm 3$