Find the common ratio of the infinite geometric series: -35-53-12527-

We take the ratio of consecutive terms: -53-35=-53 -53=259.

jmc

algebra intermediate

Problem

Find the common ratio of the infinite geometric series:

\frac{- 3}{5} - \frac{5}{3} - \frac{125}{27} - \dots

Solution

We take the ratio of consecutive terms:

\frac{\frac{- 5}{3}}{\frac{- 3}{5}} = \frac{- 5}{3} \cdot \frac{- 5}{3} = \frac{25}{9}

Final answer

\frac{25}{9}