Chapter 4.7, Problem 24PPE

To determine

To find: Whether the pattern of the sequence $10,8,6,4,\dots$ is arithmetic and also determine the common difference.

Answer to Problem 24PPE

Yes, the pattern of the sequence $10,8,6,4,\dots$ is arithmetic and the common difference is $-2$ .

Explanation of Solution

Given:

The sequence is $10,8,6,4,\dots$ .

Calculation:

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

  $8-10=-2$

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

  $6-8=-2$

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

  $4-6=-2$

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

Therefore, the common difference is $-2$ .

Thus, the pattern of the sequence $10,8,6,4,\dots$ is arithmetic and the common difference is $-2$ .