Chapter 4.6, Problem 41E

To determine

To write: the next three terms and graph the sequence.

Answer to Problem 41E

The next three terms are

  $a_1=7.5$

  $a_2=12$

  $a_3=16.5$

The graph of the sequence:

  

Explanation of Solution

Given:

The first term is 3.

The common difference is 1.5 times the first term.

Calculation:

Consider the first term of an arithmetic sequence is 3. The common difference of the sequence is 1.5 times the first term

Let us assume that the common difference is $d$

So,

  $d=1.5(3)=4.5$

Now, the second term is

  $a_1=a_0+d$

  $=3+4.5$

  $a_1=7.5$

Similarly, third term is

  $a_2=a_1+d$

  $=7.5+4.5$

  $a_2=12$

And forth term is

  $a_3=a_2+d$

  $=12+4.5$

  $a_3=16.5$

Now, draw the graph of the sequence:

  

Conclusion:

Therefore, the next three terms are

  $a_1=7.5$

  $a_2=12$

  $a_3=16.5$

The graph of the sequence is drawn.