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

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.

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 $4$ .

Unlock Step-by-Step Solutions & Ace Your Exams!

Full Textbook Solutions
Get detailed explanations and key concepts
Unlimited Al creation
Al flashcards, explanations, exams and more...
Ads-free access
To over 500 millions flashcards
Money-back guarantee
We refund you if you fail your exam.

Start your free trial

Over 30 million students worldwide already upgrade their learning with Vaia!

Recommended explanations on Math Textbooks

View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

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

Step by step solution

Step 1. Determine if the sequence is geometric.

Find the common ratio.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Mechanics Maths

Applied Mathematics

Theoretical and Mathematical Physics

Logic and Functions

Calculus

Discrete Mathematics

Study anywhere. Anytime. Across all devices.

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

Step by step solution

Step 1. Determine if the sequence is geometric.

Find the common ratio.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Mechanics Maths

Applied Mathematics

Theoretical and Mathematical Physics

Logic and Functions

Calculus

Discrete Mathematics

Study anywhere. Anytime. Across all devices.

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