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  4. If S is the sum of an infinite GP, the first term a, then the common ratio r is given by

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Q. If $S$ is the sum of an infinite GP, the first term $a$, then the common ratio $r$ is given by

J & K CETJ & K CET 2005

Solution:

Sum of an infinite $ GP=\frac{a}{1-r}=S $
$ \Rightarrow $ $ a=S(1-r) $
$ \Rightarrow $ $ a-S=-Sr $
$ \Rightarrow $ $ r=\frac{S-a}{S} $