Fifth term of a G.P. is 2 , then product of its 9 terms is

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8. Sequences and Series

easy

Fifth term of a $G.P.$ is $2$, then the product of its $9$ terms is

A

$256$

B

$512$

C

$1024$

D

None of these

(AIEEE-2002)

Solution

(b) Let the $9$ terms of a $G.P.$ is

$\frac{a}{{{r^4}}},\frac{a}{{{r^3}}},\frac{a}{{{r^2}}},\frac{a}{r},a,$ $ar,a{r^2},a{r^3},a{r^4}$.

Given, fifth term $a = 2$

Hence product of $9$ terms is ${a^9} = {(2)^9} = 512$.

Standard 11

Mathematics

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