Chapter 9.2, Problem 91E

a.

To determine

Plot the graph of the arithmetic sequence.

Answer to Problem 91E

  

Explanation of Solution

Given information:

Graph the first $10$ terms of the arithmetic sequence

  $a_n=2+3_n$ .

Calculation:

The first 10 terms of the sequence $a_n=2+3_n$ are,

  $a_1=2+3(1)$

  $=5$

  $a_2=2+3(2)$

  $=8$

  $a_3=2+3(3)$

  $=11$

  $a_4=2+3(4)$

  $=12$

  $a_5=2+3(5)$

  $=17$

  $a_6=2+3(6)$

  $20$

  $a_7=2+3(7)$

  $23$

  $a_8=2+3(8)$

  $=26$

  $a_9=2+3(9)$

  $=29$

  $a_{10}=2+3(10)$

  $=32$

Graph of these term is

  

b.

To determine

Graph the equation of the line.

Answer to Problem 91E

  

Explanation of Solution

Given information:

Graph the equation of the line $y=3x+2$ .

Calculation:

The graph of the equation, $y=3x+2$ is

  

c.

To determine

Explain the differences between the graphs.

Answer to Problem 91E

  $y=3x+2$Contains all points on the line.

  $a_n=2+3n$ Contains only points at the positive integers.

Explanation of Solution

Given information:

Discuss any differences between the graph of $a_n=2+3n$ and the graph of $y=3x+2$ .

Calculation:

Hence, the graph of the line is a continuous curve, that is, it contains all the points.

Hence, the graph of the sequence is discrete, that is, it contains only integer points.

d.

To determine

Conclude the slope of a line and the common difference of an arithmetic sequence.

Answer to Problem 91E

The slope is equal to $3$ for both the curves.

Explanation of Solution

Given information:

Compare the slope of the line in part (b) with the common difference of the sequence in part (a). What can you conclude about the slope of a line and the common difference of an arithmetic sequence?

Calculation:

We can see from the both graphs that the slopes of both the curves are same.

Hence, the slope is equal to $3$ for both the curves.