Chapter 8.2, Problem 98E

(a)

To determine

Whether the sequence is arithmetic or not.

Answer to Problem 98E

The sequence is an arithmetic sequence.

Explanation of Solution

Given information:

Given graph shown of a sequence

  

Calculation:

From the given graph observe that the sequence has the following form.

  $3,1,-1,-3,-5$

Note that the points lie on a line. This makes the sequence as an arithmetic sequence.

Therefore, the sequence is an arithmetic sequence.

(b)

To determine

Whether the common difference is 2 or not.

Answer to Problem 98E

The common difference is $-2$ .

Explanation of Solution

Given information:

Given graph shown of a sequence

  

Calculation:

The common difference is 2 is a false statement.

Because from the sequence $3,1,-1,-3,-5$ observe that the common difference is $-2$ . That is,

  $1-3=-2,-1-\left(-1\right)=-2,\mathrm{...}$

Therefore, the common difference is $-2$ .

(c)

To determine

Whether $a_1=3$ or not.

Answer to Problem 98E

The first is $a_1=3$ .

Explanation of Solution

Given information:

Given graph shown of a sequence

  

Calculation:

From the sequence $3,1,-1,-3,-5$ , observe that the first term is 3.

Therefore, the first is $a_1=3$ .