Let a_1 , a_2 ..., a_ 10 be a G.P. If a_3 a_1 = 25, then a_9 a_ 5… - Vidyadip

MCQ

Let ${a_1},{a_2}...,{a_{10}}$ be a $G.P.$ If $\frac{{{a_3}}}{{{a_1}}} = 25,$ then $\frac {{{a_9}}}{{{a_{ 5}}}}$ equal

✓
$5^4$
B
$4(5^2)$
C
$5^3$
D
$2(5^2)$

✓

Answer

Correct option: A.

$5^4$

a
$\frac{{{a_3}}}{{{a_1}}} = \frac{{{a_1}{r^2}}}{{{a_1}}} = {r^2}$

$ \Rightarrow {r^2} = 25$

Now $\frac{{{a_9}}}{{{a_5}}} = \frac{{{a_1}{r^8}}}{{{a_1}{r^4}}} = {r^4} = {\left( {25} \right)^2} = {5^4}$

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