Let ${a_n}$ be $n$th term of the GP of positive numbers. Let $\mathop \sum \limits_{n = 1}^{100} {a_{2n}} = \alpha \;$ and $\mathop \sum \limits_{n = 1}^{100} {a_{2n}} = \beta $, such that $\alpha \ne \beta ,$ then the common ratio is

$\sqrt {\frac{\alpha }{\beta }} $

$\sqrt {\frac{\beta }{\alpha }} $

JEE MATHEMATICS MCQ: SEQUENCE OF SERIES

1 Easy

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Analyzing +4 | -1

Let

{a_n}

n

th term of the GP of positive numbers. Let

\sum \limits_{n = 1}^{100} {a_{2n}} = \alpha \;

and

\sum \limits_{n = 1}^{100} {a_{2n}} = \beta

, such that

\alpha \ne \beta ,

then the common ratio is

View answer and explanation

Correct option: A

\frac{\alpha }{\beta }

Option A (

\frac{\alpha}{\beta}

) is correct because the ratio of the sum of even-indexed terms to the sum of odd-indexed terms in a GP is equal to the common ratio.

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