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Mathematics

In a Geometric Progression (G.P.) the first term is 24 and the fifth term is 8. Find the ninth term of the G.P.

AP GP

ICSE Sp 2025

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Answer

Let first term of G.P. be a and common ratio be r.

Given,

First term (a) = 24

Fifth term (ar4) = 8

⇒ar4a=824⇒r4=13⇒(r4)2=(13)2⇒r8=19.\Rightarrow \dfrac{ar^4}{a} = \dfrac{8}{24} \\[1em] \Rightarrow r^4 = \dfrac{1}{3} \Rightarrow (r^4)^2 = \Big(\dfrac{1}{3}\Big)^2 \\[1em] \Rightarrow r^8 = \dfrac{1}{9}.

By formula,

Ninth term of G.P. (a9) = ar8

= 24×19=8324 \times \dfrac{1}{9} = \dfrac{8}{3}.

Hence, ninth term of G.P. = 83\dfrac{8}{3}.

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