9.

Find the common ratio of the sequence.

–125, –25, –5, –1, . . .

100

5

–100

1 answer

To find the common ratio of a geometric sequence, you can divide any term by the previous term. In this case, the sequence is -125, -25, -5, -1, ...

Let's find the common ratio:

\[
\text{Common ratio} = \frac{\text{Second term}}{\text{First term}} = \frac{-25}{-125}
\]

\[
\frac{-25}{-125} = \frac{1}{5}
\]

It is useful to confirm it with other consecutive terms in the sequence to ensure that the ratio is consistent:

\[
\text{Common ratio} = \frac{\text{Third term}}{\text{Second term}} = \frac{-5}{-25} = \frac{1}{5}
\]

\[
\text{Common ratio} = \frac{\text{Fourth term}}{\text{Third term}} = \frac{-1}{-5} = \frac{1}{5}
\]

Since the ratio holds consistent across the terms, the common ratio of the sequence is:

\[
\boxed{\frac{1}{5}}
\]