Question

2, 1/2, 1/8, 1/32

What is the common ratio?

Answer 1

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

Let's evaluate the ratios:

1. From the first term (2) to the second term (1/2):
\[
\text{Common ratio} = \frac{1/2}{2} = \frac{1}{2} \times \frac{1}{2} = \frac{1}{4}
\]

2. From the second term (1/2) to the third term (1/8):
\[
\text{Common ratio} = \frac{1/8}{1/2} = \frac{1}{8} \times \frac{2}{1} = \frac{1}{4}
\]

3. From the third term (1/8) to the fourth term (1/32):
\[
\text{Common ratio} = \frac{1/32}{1/8} = \frac{1}{32} \times \frac{8}{1} = \frac{1}{4}
\]

Thus, the common ratio for the sequence \(2, \frac{1}{2}, \frac{1}{8}, \frac{1}{32}\) is \(\frac{1}{4}\).