Question

Find the common ratio r(r>0) of the Geometric Progression whose, sum of the third and fifth terms is $90$ and its first term is $1.$

Answer 1

The first term of the given Geometric Progression $a=1.$

Let $‘r^{\prime }$ be the common ratio of the Geometric Progression.

According to the problem,

$t_3+t_5=90$

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

$r^2+r^4=90$

$r^4+r^2–90=0$

$r^2+10r^2-9r^2-90=0$

$(r^2+10)(r^2-9)=0$

$r^2-9=0$

$r^2=9$

$r=\pm 3$

Therefore, the common ratio of the Geometric Progression is $-3$ or $3$.

Hence, this is the answer.