Question

Let $a_1, a_2, ....., a_{10}$ be a G.P. If $\frac{a_3}{a_1} = 25$, then $\frac{a_9}{a_5}$ equals :

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

Answer 1

Answer: (C)

$5^4$

Answer 2

$a_1, a_2, ....., a_{10}$ are in $G.P.,$
Let the common ratio be $r$
$\frac{a_{3}}{a_{1}} = 25 \Rightarrow \frac{a_{1}r^{2}}{a_{1}} = 25 \Rightarrow r^{2} = 25$
$\frac{a_{9}}{a_{5} } = \frac{a_{1}r^{8}}{a_{1}r^{4}} =r^{4} = 5^{4}$