Chapter 4.7, Problem 19P

Tell whether the sequence is arithmetic. If it is, identify the common difference.

$0,\frac{1}{3},\frac{2}{3},1,\dots$

To determine

To find:

That thesequence is arithmetic or not.

Answer to Problem 19P

Yes, the sequence is arithmetic and the common difference of this sequence is $\frac{1}{3}$ .

Explanation of Solution

Given information:

  $0,\frac{1}{3},\frac{2}{3},1,\mathrm{...}$

First finding the common difference in the sequence $0,\frac{1}{3},\frac{2}{3},1,\mathrm{...}$

  $\begin{array}{c}\frac{1}{3}-0=\frac{1}{3}\\ \frac{2}{3}-\frac{1}{3}=\frac{1}{3}\\ 1-\frac{2}{3}=\frac{1}{3}\end{array}$

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

The common difference of this sequence is $\frac{1}{3}$ .

Hence the sequence is arithmetic and the common difference of this sequence is $\frac{1}{3}$ .