Precalculus with Limits: A Graphing Approach, Sixth Edition
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Precalculus with Limits: A Graphing Approach, Sixth Edition View details
3. Geometric Sequences and Series
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Exercise 1 Page 595

What types of sequences do you know?

geometric, common

We want to complete the following statement.

A sequence is called a sequence if the ratios of consecutive terms are the same. This ratio is called the ratio.

Let's start by recalling two types of sequences we learned in this chapter.

Type of Sequence Description
arithmetic sequence A sequence is arithmetic when the differences between consecutive terms are the same. This difference is the common difference of the sequence.
geometric sequence A sequence is geometric when the ratios of consecutive terms are the same. This ratio is the common ratio of the sequence.

We can see that the given sentence matches the description of the geometric sequence. With this in mind, let's complete the sentence.

A sequence is called a geometric sequence if the ratios of consecutive terms are the same. This ratio is called the common ratio.