Question

What is the common ratio of the geometric sequence below?

–2, 4, –8, 16, –32, ...

Answer 1

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

In the given sequence: -2, 4, -8, 16, -32, ...

Let's calculate the common ratio \( r \) using the first two terms:

\[
r = \frac{4}{-2} = -2
\]

Now, let's check this ratio with the next pair of terms:

\[
r = \frac{-8}{4} = -2
\]

And the next pair:

\[
r = \frac{16}{-8} = -2
\]

And one more pair:

\[
r = \frac{-32}{16} = -2
\]

In all cases, the common ratio is consistent. Therefore, the common ratio of the geometric sequence is:

\[
\boxed{-2}
\]