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

Question

asked Apr 24, 2020 50.0k views

1 Answer

Bernardo Duarte · Answer 1 · 2020-05-01T03:52:55+0000

Answer:

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,

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