14.

Find the common ratio of the sequence.

–164, –82, –41, –20.5, . . .

82

–82

2

1 answer

To find the common ratio of a geometric sequence, we divide any term by the preceding term.

Given the sequence: –164, –82, –41, –20.5, ...

Let's calculate the common ratio (\(r\)) between the terms:

\[
r = \frac{{\text{{second term}}}}{\text{{first term}}} = \frac{{-82}}{-164} = \frac{1}{2}
\]

Let's verify with the next term to ensure consistency:

\[
r = \frac{{\text{{third term}}}}{\text{{second term}}} = \frac{{-41}}{-82} = \frac{1}{2}
\]

And checking one more time:

\[
r = \frac{{\text{{fourth term}}}}{\text{{third term}}} = \frac{{-20.5}}{-41} = \frac{1}{2}
\]

The common ratio for the given sequence is \( \frac{1}{2} \) or 0.5.