Chapter 3.6, Problem 15PPS

To determine

To find the next three terms of the arithmetic sequence.

Answer to Problem 15PPS

  $\frac{3}{2},2,\frac{5}{2}$

Explanation of Solution

Given:

Sequence:

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

Concept used:

An arithmetic sequence is a sequence of numbers such that the difference between the consecutive terms is constant.

Calculation:

The common difference of the arithmetic sequence is:

  $0-\left(-\frac{1}{2}\right)=\frac{1}{2}$

Now, the next three consecutive numbers are:

  $\begin{array}{l}1+\left(\frac{1}{2}\right)=\frac{3}{2}\\ \frac{3}{2}+\left(\frac{1}{2}\right)=2\\ 2+\left(\frac{1}{2}\right)=\frac{5}{2}\end{array}$

Conclusion:

Therefore, the next three terms of the arithmetic sequence: $\frac{3}{2},2,\frac{5}{2}$ .