Question

What is the common ratio for this geometric sequence?
64, 16, 4, 1,…
A. 1/8
B. 1/4
C. 4
D. 8

Answer 1

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

For the sequence \(64, 16, 4, 1, \ldots\):

1. The common ratio \(r\) can be found by dividing the second term by the first term:
\[
r = \frac{16}{64} = \frac{1}{4}
\]

2. We can verify this with the next terms:
\[
\frac{4}{16} = \frac{1}{4}, \quad \text{and} \quad \frac{1}{4} = \frac{1}{4}
\]

Since the common ratio is consistent throughout, the common ratio for the given geometric sequence is \(\frac{1}{4}\).

Therefore, the answer is:
**B. 1/4**