Chapter 4.7, Problem 27PPE

To determine

To find: Whether the pattern of the sequence $15,14.5,14,13.5,13,\dots$ is arithmetic and also determine the common difference.

Answer to Problem 27PPE

Yes, the pattern of the sequence $15,14.5,14,13.5,13,\dots$ is arithmetic and the common difference is $-0.5$ .

Explanation of Solution

Given:

The sequence is $15,14.5,14,13.5,13,\dots$ .

Calculation:

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

  $14.5-15=-0.5$

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

  $14-14.5=-0.5$

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

  $13.5-14=-0.5$

Since the difference is same, therefore, the sequence is arithmetic progression.

Therefore, the common difference is $-0.5$ .

Thus, the pattern of the sequence $15,14.5,14,13.5,13,\dots$ is arithmetic and the common difference is $-0.5$ .