Question

Find the common ratio for this geometric sequence.
72, 12, 2, 1/3 , 1/8

A. 1/3
B. 6
C. 1/6
D. 3

Answer 1

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

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

\[
\text{Common Ratio} = \frac{\text{Second term}}{\text{First term}} = \frac{12}{72} = \frac{1}{6}
\]

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

For the second and third terms:

\[
\frac{\text{Third term}}{\text{Second term}} = \frac{2}{12} = \frac{1}{6}
\]

For the third and fourth terms:

\[
\frac{\text{Fourth term}}{\text{Third term}} = \frac{\frac{1}{3}}{2} = \frac{1}{3} \times \frac{1}{2} = \frac{1}{6}
\]

For the fourth and fifth terms:

\[
\frac{\text{Fifth term}}{\text{Fourth term}} = \frac{\frac{1}{8}}{\frac{1}{3}} = \frac{1}{8} \times 3 = \frac{3}{8}
\]

All calculations confirm that the common ratio is consistent. Therefore, the common ratio for the geometric sequence is:

\[
\boxed{\frac{1}{6}}
\]

So, the answer is **C. 1/6**.