What is the common ratio of the geometric sequence below?

18，-6,2，-2/3..

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.

What is the common ratio of the geometric sequence below? 18, -6, 2, -2/3...

Discover how to find the common ratio of a geometric sequence with the terms 18, -6, 2, and -2/3. This problem explores key mathematical concepts such as geometric sequences and the common ratio formula. Suitable for students in Grades 8-10.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation