Chapter 4.7, Problem 9PPE

To determine

To find: The pattern of the sequence $6,13,20,27,\dots$ and the next two terms.

Answer to Problem 9PPE

The pattern of the sequence $6,13,20,27,\dots$ is arithmetic progression and the next two terms are 34 and 41.

Explanation of Solution

Given:

The sequence is $6,13,20,27,\dots$ .

Calculation:

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

  $13-6=7$

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

  $20-13=7$

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

  $27-20=7$

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

The next two terms are the sum of the number and the common difference as follows:

  $\begin{array}{l}27+7=34\\ 34+7=41\end{array}$

Thus, the pattern of the sequence $6,13,20,27,\dots$ is arithmetic progression and the next two terms are 34 and 41.