If sum of an infinite G.P. be 9 and sum of first two terms be 5 , then common ratio is

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8. Sequences and Series

easy

If the sum of an infinite $G.P.$ be $9$ and the sum of first two terms be $5$, then the common ratio is

A

$1/3$

B

$3/2$

C

$3/4$

D

$2/3$

Solution

(d) Infinite series is $a,\;ar,\;a{r^2}……..\infty $

Sum $S = \frac{a}{{1 – r}} = 9 $

$\Rightarrow a = 9(1 – r)$ …..$(i)$

and $a + ar = 5$

$ \Rightarrow a(1 + r) = 5 $

$\Rightarrow 9(1 – r)(1 + r) = 5$ [By equation $(i)$]

$1 – r^2 = \frac{{5}}{{9}}$

$\Rightarrow r = \pm \frac{{2}}{{3}}$

Standard 11

Mathematics

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