First term of a G.P. whose second term is 2 and sum to infinity is 8 , will be

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8. Sequences and Series

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The first term of a $G.P.$ whose second term is $2$ and sum to infinity is $8$, will be

A

$6$

B

$3$

C

$4$

D

$1$

Solution

(c) We have $ar = 2$ and ${S_\infty } = 8 = \frac{a}{{1 – r}}$

$ \Rightarrow $ $8 = \frac{2}{{r(1 – r)}}\left( {\;a = \frac{2}{r}} \right)$

$ \Rightarrow $ $4r(1 – r) = 1 $

$\Rightarrow 4r – 4{r^2} – 1 = 0$

$ \Rightarrow $ $4{r^2} – 4r + 1 = 0$

$\Rightarrow \left( {r – \frac{1}{2}} \right)(4r – 2) = 0$

$\Rightarrow r = \frac{1}{2}$

So first term $a = 4$.

Standard 11

Mathematics

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