Question

If $a_1,a_2,a_3,\dots ,a_{10}$ is a geometric progression and $\frac{a_3}{a_1}=25$, then $\frac{a_9}{a_5}$ equals

• A. $3\left(5^2\right)$
• B. $5^3$
• C. $5^4$
• D. $2\left(5^2\right)$

Answer 1

Answer: (C)

$\frac{a_3}{a_1}=25$
$\frac{a{r}^2}{a}=25$
$r^2=5^2$
$\frac{a_4}{a_5}=\frac{a{r}^8}{a{r}^4}=r^4=5^4$