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:
\[
\boxed{\frac{1}{5}}
\]
9.
Find the common ratio of the sequence.
–125, –25, –5, –1, . . .
100
5
–100
1 answer