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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 127 (page 1198)

In the following exercise, determine if the sequence is geometric, and if so, indicate the common ratio.
$3, 12, 48, 192, 768, 3072, . . .$

Short Answer

Expert verified

Yes, the sequence is geometric with common ratio equal to $4$ .

Step by step solution

01

Step 1. Determine if the sequence is geometric.

Consider the sequence $3, 12, 48, 192, 768, 3072, . . .$

The sequence is said to be geometric sequence if the ratio between the consecutive terms is equal.

role="math" localid="1645298916718" $\begin{array}{rcl} \frac{12}{3} & = & 4 \\ \frac{48}{12} & = & 4 \\ \frac{192}{48} & = & 4 \\ \frac{768}{192} & = & 4 \\ \frac{3072}{768} & = & 4 \end{array}$

As the ratio is constant between the consecutive terms, the sequence is a geometric sequence.

02

Find the common ratio.

As $\begin{array}{rcl} \frac{12}{3} \end{array} = \begin{array}{rcl} \frac{48}{12} \end{array} = \begin{array}{rcl} \frac{192}{48} \end{array} \begin{array}{rcl} = \end{array} \begin{array}{rcl} \frac{768}{192} \end{array} \begin{array}{rcl} = \end{array} \begin{array}{rcl} \frac{3072}{768} \end{array} \begin{array}{rcl} = \end{array} \begin{array}{rcl} 4 \end{array}$ , common ratio is $4$ .

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