Question

Find the common ratio of the geometric sequence: 2, 6, 18, 54, . . . (1 point)
The common ratio is
.

Answer 1

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

In this sequence:
- The first term \( a_1 = 2 \)
- The second term \( a_2 = 6 \)

Calculating the common ratio \( r \):

\[
r = \frac{a_2}{a_1} = \frac{6}{2} = 3
\]

To confirm, we can check the ratio of the next terms:
- The third term \( a_3 = 18 \)

\[
r = \frac{a_3}{a_2} = \frac{18}{6} = 3
\]

- The fourth term \( a_4 = 54 \)

\[
r = \frac{a_4}{a_3} = \frac{54}{18} = 3
\]

Since the ratio is consistently 3, the common ratio is:

\[
\text{The common ratio is } 3.
\]