Answer
See explanations, $\frac{1}{r}$
Work Step by Step
Step 1. Given $a_n$ is a geometric sequence with common ration $r$, we have $\frac{a_{n+1}}{a_n}=r$
Step 2. Examine the sequence $b_n=\frac{1}{a_n}$, the ration $\frac{b_{n+1}}{b_n}=\frac{1/a_{n+1}}{1/a_n}=\frac{a_n}{a_{n+1}}=\frac{1}{r}$
Step 3. We proved that the sequence $b_n=\frac{1}{a_n}$ is also geometric with a common ratio of $r'=\frac{1}{r}$
