Question

Find the common ratio for this geometric sequence.
8,2, 1/2, 1/8, 1/32

A. 4
B. 1/4
C. 1/2
D. 2

Answer 1

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

Let's calculate the common ratio using the first two terms:

\[
r = \frac{2}{8} = \frac{1}{4}
\]

Now let's verify by calculating the ratio of other consecutive terms:

- For the second and third terms:
\[
r = \frac{1/2}{2} = \frac{1}{4}
\]

- For the third and fourth terms:
\[
r = \frac{1/8}{1/2} = \frac{1/8 \times 2}{1} = \frac{2}{8} = \frac{1}{4}
\]

- For the fourth and fifth terms:
\[
r = \frac{1/32}{1/8} = \frac{1/32 \times 8}{1} = \frac{8}{32} = \frac{1}{4}
\]

In all cases, the common ratio is \(\frac{1}{4}\).

Thus, the common ratio for this geometric sequence is:

**B. \(\frac{1}{4}\)**