If the sum of an infinite GP be 9 and sum of first two terms be 5 then their common ratio is …..

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If the sum of an infinite GP be 9 and sum of first two terms be 5 then their common ratio is …..

MathematicsSequences and SeriesMHT CETMHT CET 2019 (Shift 2)

Options:

A $\frac{1}{3}$
B 3
C $\frac{2}{3}$
D $\frac{3}{2}$

Solution:

2259 Upvotes Verified Answer

The correct answer is:

\frac{2}{3}

We have,
Sum of infinite GP,

\frac{a}{1 - r} = 9

\Rightarrow a + a r = 5

\Rightarrow a (1 + r) = 5

\Rightarrow 9 (1 - r) (1 + r) = 5

\Rightarrow 1 - r^{2} = \frac{5}{9} \Rightarrow r^{2} = \frac{4}{9} \Rightarrow r = \frac{2}{3}

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