Question

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

Answer 1

Answer:

Common ratio r = 0.5

Step-by-step 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

$S=\dfrac{b_1}{1-r}$

Hence,

$0.54=\dfrac{0.27}{1-r}\\ \\1-r=\dfrac{0.27}{0.54}=\dfrac{27}{54}=\dfrac{1}{2}=0.5\\ \\r=1-0.5=0.5$