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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 12.41 (page 1187)

Determine if each sequence is geometric. If so indicate the common ratio.
鈸�. $7, 21, 63, 189, 567, 1, 701, 鈥�$
鈸�. $64, 16, 4, 1, 1 4, 1 16, 鈥�$
鈸�. $2, 4, 12, 48, 240, 1, 440, 鈥�$

Short Answer

Expert verified

鈸�. Yes, the sequence is geometric with common ratio equal to $3$ .

鈸�. Yes, the sequence is geometric with common ratio equal to $\frac{1}{4}$

鈸�. No, the sequence is not geometric.

Step by step solution

01

Step 1. Given information

Sequences are as follows:

鈸� $7, 21, 63, 189, 567, 1, 701, 鈥�$

鈸� $64, 16, 4, 1, 1 4, 1 16, 鈥�$

鈸� $2, 4, 12, 48, 240, 1, 440, 鈥�$

02

Step 2. Determine if each sequence is geometric. If so indicate the common ratio.

A sequence is said to be geometric if ratio of the consecutive terms is same.

鈸� $7, 21, 63, 189, 567, 1, 701, . . .$

role="math" localid="1645264969253" $\begin{array}{rcl} \frac{21}{7} & = & 3 \\ \frac{63}{21} & = & 3 \\ \frac{189}{63} & = & 3 \\ \frac{567}{189} & = & 3 \\ \frac{1701}{567} & = & 3 \end{array}$

So, the sequence is geometric and common ratio is equal to $3$

03

Step 3. Determine if each sequence is geometric. If so indicate the common ratio.

鈸� $64, 16, 4, 1, \frac{1}{4}, \frac{1}{16}, . . .$

$\frac{16}{64} = \frac{1}{4} \frac{4}{16} = \frac{1}{4} \frac{1}{4} = \frac{1}{4} \frac{\frac{1}{4}}{1} = \frac{1}{4} \frac{\frac{1}{16}}{\frac{1}{4}} = \frac{1}{4}$

So, the ratio of consecutive terms is same.

Yes, the sequence is geometric with common ratio equal to $\frac{1}{4}$

04

Step 4. Determine if each sequence is geometric. If so indicate the common ratio.

鈸� $2, 4, 12, 48, 240, 1, 440, . . .$

role="math" $\begin{array}{rcl} \frac{4}{2} & = & 2 \\ \frac{12}{4} & = & 3 \end{array}$

As $\frac{4}{2} 鈮� \frac{12}{4}$ , the sequence is not geometric.

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Most popular questions from this chapter

Find a general term for the sequence whose first five terms are shown $\frac{1}{2}, \frac{1}{4}, \frac{1}{8}, \frac{1}{16}, \frac{1}{32}, 鈥�$

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In the following exercises, determine if each sequence is arithmetic, and if so, indicate the common difference.

$13, 9, 5, 1, 鈭� 3, 鈭� 7, . . . . .$

In the following exercises, determine if each sequence is arithmetic, and if so, indicate the common difference.

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