Question

Find the common ratio r of an infinite geometric series with sum S=7 and first term 4.​

Answer 1

Given ,

Sum of infinte terms of GP (S) = 7

First term (a) = 4

We know that , the sum of infinite terms of geometric progression (GP) is given by

$\boxed{ \tt{S = \frac{a}{(1 - r)} }}$

Thus ,

$\tt \hookrightarrow 7 = \frac{4}{1 -r }$

$\tt \hookrightarrow 7 - 7r = 4$

$\tt \hookrightarrow - 7r = - 3$

$\tt \hookrightarrow r = \frac{3}{7}$

Hence , the common ratio of GP is 3/7