Chapter 12: Q 138. (page 1198)

In the following exercises, determine if each sequence is arithmetic, geometric or neither. If arithmetic, indicate the common difference. If geometric, indicate the common ratio.
$4, 8, 12, 24, 48, 96, . . .$

Short Answer

Expert verified

The sequence is neither.

Step by step solution

Step 1. Write the given sequence and use the definition of geometric sequence

The given sequence is:

$4, 8, 12, 24, 48, 96, . . .$

A geometric sequence is a sequence where the ratio between consecutive terms is always the same.

The ratio between consecutive terms, $\frac{a_{n}}{a_{n - 1}}$ , is $r$ , the common ratio, where $r$ is greater than or equal to two.

Step 2. Find the ratio of the consecutive terms.

$\frac{8}{4} = 2, \frac{12}{8} = \frac{3}{2}, \frac{24}{12} = 2, \frac{48}{24} = 2, \frac{96}{48} = 2$

As we can see that the ratio of consecutive terms is not the same, therefore this sequence is not geometric.

Step 3. To determine if the sequence is arithmetic, find the difference of consecutive terms

$8 - 4 = 4, 12 - 8 = 4, 24 - 12 = 12, 48 - 24 = 24, 96 - 48 = 48$

As we can see that the difference of consecutive terms is not the same, therefore this sequence is not arithmetic.

This sequence is neither.

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In the following exercises, determine if each sequence is arithmetic, geometric or neither. If arithmetic, indicate the common difference. If geometric, indicate the common ratio.
$4, 8, 12, 24, 48, 96, . . .$

Short Answer

Step by step solution

Step 1. Write the given sequence and use the definition of geometric sequence

Step 2. Find the ratio of the consecutive terms.

Step 3. To determine if the sequence is arithmetic, find the difference of consecutive terms

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In the following exercises, determine if each sequence is arithmetic, geometric or neither. If arithmetic, indicate the common difference. If geometric, indicate the common ratio.4,8,12,24,48,96,...

Short Answer

Step by step solution

Step 1. Write the given sequence and use the definition of geometric sequence

Step 2. Find the ratio of the consecutive terms.

Step 3. To determine if the sequence is arithmetic, find the difference of consecutive terms

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Probability and Statistics

Geometry

Decision Maths

Statistics

Mechanics Maths

Calculus

Study anywhere. Anytime. Across all devices.

In the following exercises, determine if each sequence is arithmetic, geometric or neither. If arithmetic, indicate the common difference. If geometric, indicate the common ratio.
$4, 8, 12, 24, 48, 96, . . .$