Let a 1 , a 2 , … , a 10 be a G.P. If a 1 a 3 = 25 , then a 5 a 9 equals :

Let a 1 = a , a 2 = a r , a 3 = a r 2 … a 10 = a r 9 where r = common ratio of given G.P. Given, a 1 a 3 = 25 ⇒ a a r 2 = 25 ⇒ r = ± 5 Now, a 5 a 9 = a r 4 a r 8 = r 4 = ( ± 5 ) 4 = 5 4

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MathematicsSequence & SeriesG.P.Easy2 minPYQ_2019

MathematicsEasystatement

Let $a_{1}, a_{2}, \dots, a_{10}$ be a G.P. If $\frac{a _{3}}{a _{1}} = 25,$ then $\frac{a _{9}}{a _{5}}$ equals :

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Solution:

Let $a_{1} = a, a_{2} = a r, a_{3} = a r^{2} \dots a_{10} = a r^{9}$ where $r =$ common ratio of given G.P. Given, $\frac{a _{3}}{a _{1}} = 25$ $\Rightarrow \frac{a r ^{2}}{a} = 25$ $\Rightarrow r = \pm 5$ Now, $\frac{a _{9}}{a _{5}} = \frac{a r ^{8}}{a r ^{4}} = r^{4} = (\pm 5)^{4} = 5^{4}$

Stream:JEESubject:MathematicsTopic:Sequence & SeriesSubtopic:G.P.

⏱ 2mℹ️ Source: PYQ_2019

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