Question

How do you find the common ratio of an infinite geometric series?

Answer 1

You can find the common ratio `r` by finding the ratio between any two consecutive terms.

`r=a_1/a_0=a_2/a_1=a_3/a_2=cdots=a_{n+1}/a_n=cdots`

For the geometric series `sum_{n=0}^infty(-1)^n{2^{2n}}/5^n`, the common ratio

`r=a_1/a_0={-2^2/5}/{1}=-4/5`