Chapter 4.7, Problem 28PPE

To determine

To find: Whether the pattern of the sequence $4,4.4,4.44,4.444,\dots$ is arithmetic and also determine the common difference.

Answer to Problem 28PPE

No, the pattern of the sequence $4,4.4,4.44,4.444,\dots$ is not arithmetic.

Explanation of Solution

Given:

The sequence is $4,4.4,4.44,4.444,\dots$ .

Calculation:

Subtract the first term from the second term to obtain the difference.

  $4.4-4=0.4$

Subtract the second term from the third term to obtain the difference.

  $4.44-4.4=0.04$

Subtract the third term from the fourth term to obtain the difference.

  $4.444-4.44=0.004$

Since the difference is not same, therefore, the sequence is not an arithmetic progression.

Thus, the pattern of the sequence $4,4.4,4.44,4.444,\dots$ is not arithmetic.