Chapter 3.6, Problem 6CYU

To determine

To write: the $n^{th}$ term of the given arithmetic sequence and to graph the first five terms.

Explanation of Solution

Given information:

Consider the sequence $-1,-0.5,0,0.5,\mathrm{............}$

Calculations:

Consider the arithmetic sequence $-1,-0.5,0,0.5,\mathrm{............}$

Common difference $d=0+0.5=\mathrm{0.5.}$

First term $a=-1$

  $\begin{array}{l}{a}_n=a+(n-1)d\\ =-1+(n-1)(0.5)\\ =-1+0.5n-0.5\\ =-1.5+0.5n\end{array}$

Hence, the $n^{th}$ term of the sequence is $a_n=-1.5+0.5n$

The graph of the sequence is $-1,-0.5,0,0.5,\mathrm{............}$

  

Hence, the first five terms of the given sequence is given below.