Let the function
Question:

Let $\mathrm{a}_{1}, \mathrm{a}_{2}, \ldots ., \mathrm{a}_{10}$ be a G.P. If $\frac{\mathrm{a}_{3}}{\mathrm{a}_{1}}=25$, then

$\frac{a_{9}}{a_{5}}$ equals:

1. $2\left(5^{2}\right)$

2. $4\left(5^{2}\right)$

3. $5^{4}$

4. $5^{3}$

Correct Option: , 3

Solution:

$\mathrm{a}_{1}, \mathrm{a}_{2}, \ldots . . \mathrm{a}_{10}$ are in G.P.,

Let the common ratio be r

$\frac{\mathrm{a}_{3}}{\mathrm{a}_{1}}=25 \Rightarrow \frac{\mathrm{a}_{1} \mathrm{r}^{2}}{\mathrm{a}_{1}}=25 \Rightarrow \mathrm{r}^{2}=25$

$\frac{a_{9}}{a_{5}}=\frac{a_{1} r^{8}}{a_{1} r^{4}}=r^{4}=5^{4}$