Chapter 4.7, Problem 1LC

To determine

To find: The pattern of the sequence $3,11,19,27,\dots$ and the next two terms.

Answer to Problem 1LC

The pattern of the sequence $3,11,19,27,\dots$ is arithmetic progression and the next two terms are 35 and 43.

Explanation of Solution

Given:

The sequence is $3,11,19,27,\dots$ .

Calculation:

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

  $11-3=8$

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

  $19-11=8$

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

  $27-19=8$

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:

  $\begin{array}{l}27+8=35\\ 35+8=43\end{array}$

Thus, the pattern of the sequence $3,11,19,27,\dots$ is arithmetic progression and the next two terms are 35 and 43.