Chapter 8.2, Problem 92E

(a)

To determine

To find: The required arithmetic sequence.

Answer to Problem 92E

The points lie on a line in the graph so the sequence is arithmetic.

Explanation of Solution

Given:

The given graph of the sequence is shown in Figure 1

  

Figure 1

Calculation:

From the given graph the sequence is $3,1,-1,-3,-5$ .

The sequence and the graph shows that he point lie on the line thus, the sequence is arithmetic sequence.

(b)

To determine

To Prove: The common difference is two.

Explanation of Solution

Given:

The given graph of the sequence is shown in Figure 1

  

Figure 1

Calculation:

Consider the general formula for the arithmetic sequence is,

  $a_n=a_1+\left(n-1\right)d$

Then,

  $\begin{array}{l}-5=3+\left(5-1\right)d\\ d=\frac{-8}{4}\\ d=-2\end{array}$

Hence, Proved.

(c)

To determine

To Prove: The first term of the sequence is $3$ .

Explanation of Solution

Given:

The given graph of the sequence is shown in Figure 1

  

Figure 1

Calculation:

From the graph shown in Figure 1 it is clear that the first term of the sequence is $3$ .

Hence, Proved.