Sum of infinite number of terms in G.P. is 20 and sum of their square is 100 . common ratio of G.P.

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8. Sequences and Series

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Sum of infinite number of terms in $G.P.$ is $20$ and sum of their square is $100$. The common ratio of $G.P.$ is

A

$5$

B

$3/5$

C

$8/5$

D

$1/5$

(AIEEE-2002)

Solution

(b) $\frac{a}{{1 – r}} = 20 …..(i)$

$\frac{{{a^2}}}{{1 – {r^2}}} = 100 …..(ii)$

From $(i)$ and $(ii),$

$\frac{a}{{1 + r}} = 5$, $\left[ {a = 20(1 – r)\,\,{\rm{by}}\,\,(i)} \right]$

==> $\frac{{20(1 – r)}}{{1 + r}} = 5$

$ \Rightarrow 5r = 3$

==> $r = 3/5$.

Standard 11

Mathematics

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