Question

What is the common ratio in the following geometric sequence?

2, 1/2, 1/8, 1/32,...
(1 point)
Responses

-1.5
-1.5

4
4

1/2
1 half

1/4

Answer 1

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

For the sequence \(2, \frac{1}{2}, \frac{1}{8}, \frac{1}{32},...\):

1. Divide the second term by the first term:
\[
\frac{1/2}{2} = \frac{1}{2} \div 2 = \frac{1}{2} \times \frac{1}{2} = \frac{1}{4}
\]

2. Divide the third term by the second term:
\[
\frac{1/8}{1/2} = \frac{1}{8} \div \frac{1}{2} = \frac{1}{8} \times \frac{2}{1} = \frac{1}{4}
\]

3. Divide the fourth term by the third term:
\[
\frac{1/32}{1/8} = \frac{1}{32} \div \frac{1}{8} = \frac{1}{32} \times \frac{8}{1} = \frac{1}{4}
\]

In each case, the common ratio is \(\frac{1}{4}\).

Thus, the common ratio of the sequence is:

**1/4**