   Chapter 13.3, Problem 18E ### Algebra and Trigonometry (MindTap ...

4th Edition
James Stewart + 2 others
ISBN: 9781305071742

#### Solutions

Chapter
Section ### Algebra and Trigonometry (MindTap ...

4th Edition
James Stewart + 2 others
ISBN: 9781305071742
Textbook Problem

# SKILLS13-22 ■ Geometric Sequence? The first four terms of a sequence are given. Determine whether these terms can be the terms of a geometric sequence. If the sequence is geometric, find the common ratio. 27 , − 9 , 3 , − 1 , …

To determine

Whether the sequence 27,9,3,1, is a geometric sequence and the common difference when the sequence is a geometric sequence.

Explanation

Approach:

A geometric sequence is the sequence of the form,

a,ar,ar2,ar3,

Here, a is the first term and r is the common ratio which is the ratio of two consecutive terms.

Calculation:

Consider the sequence,

27,9,3,1,

Since in the geometric sequence, any two consecutive terms of the sequence ratio be r. then,

Calculate the common ratio of second and first terms.

r=927=13

Calculate the common ratio of third and second terms.

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