Find the common ratio of the infinite geometric series: 56-49+32135-

We take the ratio of consecutive terms: -4956=-49 65=-815.

jmc

algebra intermediate

Problem

Find the common ratio of the infinite geometric series:

\frac{5}{6} - \frac{4}{9} + \frac{32}{135} - \dots

Solution

We take the ratio of consecutive terms:

\frac{- \frac{4}{9}}{\frac{5}{6}} = \frac{- 4}{9} \cdot \frac{6}{5} = - \frac{8}{15} .

Final answer

-\frac{8}{15}