Question

Obtain the common ratio of the geometric series 0.27+...=54%​

Answer 1

Common ratio r = 0.5

Explanation:

Given the geometric series 0.27 + ...

This is infinite geometric series with
`b_1=0.27,` unknown common rate r and sum S of 54% that is 0.54 as decimal.

Use formula

`S=(b_1)/(1-r)`

Hence,

`0.54=(0.27)/(1-r)\\ \\1-r=(0.27)/(0.54)=(27)/(54)=(1)/(2)=0.5\\ \\r=1-0.5=0.5`