Question

Find the common ratio of the GP whose, sum of the fifth and third terms is 90 and its first term is 1.

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

Answer 1

The correct option is B $\pm 3$

The first term of the given GP $a=1$.

Let r be the common ratio of the geometric progression.

According to the problem,

$t_3+t_5=90$

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

$r^2+r^4=90$

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

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

$r^2-9=0$

$r^2=9$

$r=\pm 3$

Therefore, the common ratio of the G.P. is $-3$ or $3$.