If first term of a G.P. be 5 and common ratio be - 5 , then which term is 3125

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8. Sequences and Series

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If the first term of a $G.P.$ be $5$ and common ratio be $ - 5$, then which term is $3125$

A

${6^{th}}$

B

${5^{th}}$

C

${7^{th}}$

D

${8^{th}}$

Solution

(b) Given that first term $a = 5$ and common ratio $r = – 5$.

Suppose that ${n^{th}}$ term is $3125,$

then $a{r^{n – 1}} = 3125$

$\Rightarrow 5{( – 5)^{n – 1}} = 3125 $

$\Rightarrow {( – 5)^{n – 1}} = {5^4}$

Hence $ n=5 $.

Standard 11

Mathematics

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