First slide

Geometric progression

Question

$Let a_{n} be the n^{th} term of the G.P of positive numbers. Let \sum_{n = 1}^{100} a_{2 n} = α and \sum_{n = 1}^{100} a_{2 n - 1} = β$ $such that α \neq β, then the common ratio is$

Moderate

A

$\frac{α}{β}$
B

$\frac{β}{α}$
C

$\sqrt{\frac{α}{β}}$
D

$\sqrt{\frac{β}{α}}$

Solution

$\begin{array}{l} Let 'a' be the first term and ' r' the common ratio of given G.P then \\ α = \sum_{n = 1}^{100} a_{2 n} α = \frac{ar (1 - r^{200})}{1 - r^{2}} β = \frac{a (1 - r^{200})}{1 - r^{2}} \Rightarrow \frac{α}{β} = r \end{array}$

Get Instant Solutions

When in doubt download our app. Now available Google Play Store- Doubts App

Recieve an sms with download link

Doubts App

OR

SCAN ME

Doubts App

Doubts App