Chapter 4.7, Problem 29PPE

To determine

To find: Whether the pattern of the sequence $-3,-7,-10,-14,\dots$ is arithmetic and also determine the common difference.

Answer to Problem 29PPE

Yes, the pattern of the sequence $-3,-7,-10,-14,\dots$ is arithmetic and the common difference is $-4$ .

Explanation of Solution

Given:

The sequence is $-3,-7,-10,-14,\dots$ .

Calculation:

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

  $-7+3=-4$

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

  $-10+7=-4$

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

  $-14+10=-4$

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

Therefore, the common difference is $-4$ .

Thus, the pattern of the sequence $-3,-7,-10,-14,\dots$ is arithmetic and the common difference is $-4$ .