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Intermediate Algebra

OPENSTAX

$Math Studyset 91影视 Explanations$ Math

OER 2017 Edition 路 1346 pages

ISBN: 9780998625720

Chapter 12: Q 130. (page 1198)

In the exercise, determine if the sequence is geometric, and if so, indicate the common ratio.
$54, 18, 6, 2, \frac{2}{3}, \frac{2}{9}, . . .$

Short Answer

Expert verified

The sequence is geometric with common ratio equal to $\frac{1}{3}$ .

Step by step solution

01

Step 1. Given information

The sequence is $54, 18, 6, 2, \frac{2}{3}, \frac{2}{9}, . . .$

02

Step 2. Determine if the sequence is geometric, and if so, indicate the common ratio.

Consider the sequence $54, 18, 6, 2, \frac{2}{3}, \frac{2}{9}, . . .$

$\frac{18}{54} = \frac{1}{3} \frac{6}{18} = \frac{1}{3} \frac{2}{6} = \frac{1}{3} \frac{\frac{2}{3}}{2} = \frac{1}{3} \frac{\frac{2}{9}}{\frac{2}{3}} = \frac{1}{3}$

So, the sequence is geometric with common ratio equal to $\frac{1}{3}$

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