Chapter 7, Problem 1T

Solution

To identify: Whether the sequence is arithmetic, geometric, or neither $5,9,13,17,\mathrm{...}$ .

The given sequence is an arithmetic sequence.

Given information:

The given sequence is $5,9,13,17,\mathrm{...}$ .

Explanation:

Consider the given sequence,

  $5,9,13,17,\mathrm{...}$

Firstly check if the given sequence is an arithmetic sequence or not. For doing so find the common difference of the consecutive term if the difference is constant then the sequence will be called an arithmetic sequence.

The common difference ( d ) is:

  $\begin{array}{c}9-5=4\\ 13-9=4\\ 17-13=4\end{array}$

The given sequence is arithmetic sequence because the common difference of two successive terms is a constant.

Therefore, $5,9,13,17,\mathrm{...}$ is an arithmetic sequence.