To find the common ratio $r$ of a geometric sequence, we divide any term by the preceding term.

The terms of the sequence are:

$18, -6, 2, -\frac{2}{3}, \dots$

Let's calculate the common ratio step by step:

1. Divide the second term by the first term: $r = \frac{-6}{18} = -\frac{1}{3}$

2. Divide the third term by the second term: $r = \frac{2}{-6} = -\frac{1}{3}$

3. Divide the fourth term by the third term: $r = \frac{-\frac{2}{3}}{2} = -\frac{1}{3}$

Since the ratio between consecutive terms is the same, the common ratio is: $r = -\frac{1}{3}$

Would you like further details on how to work with geometric sequences?

Here are some related questions:

1. How do you find the nth term of a geometric sequence?
2. How do you determine the sum of a geometric series?
3. What are the conditions for the convergence of an infinite geometric series?
4. How does the common ratio affect the growth or decay of a geometric sequence?
5. How can you find the common ratio if not all terms of the sequence are given?

Tip: In geometric sequences, if the common ratio is negative, the terms alternate between positive and negative.