1. Tardigrade
  2. Question
  3. Mathematics
  4. If the term of an infinite G.P. is equal to twice the sum of all the terms that follows it, then the common ratio is

Question Error Report

Thank you for reporting, we will resolve it shortly

Back to Question

Q. If the term of an infinite G.P. is equal to twice the sum of all the terms that follows it, then the common ratio is

Sequences and Series

Solution:

By the given condition
$a= 2\left[ar+ar^{2}+ar^{3}+.......\right] $
$ \therefore a= 2 \frac{ar}{1-r} $
$\Rightarrow 1= \frac{2r}{1-r} $
$ \Rightarrow 1-r = 2r $
$\Rightarrow 3r= 1 $
$ \Rightarrow r= \frac{1}{3}$ .