Chapter 6, Problem 33CR

To determine

To find:The first six terms of the sequence. Graph the sequence.

Answer to Problem 33CR

The first six terms of the sequence are $-4,12,-36,108,-324,972$ .

Graph of the sequence is

  

Explanation of Solution

Giveninformation:

The recurece relation is $a_1=-4,a_n=-3a_{n-1}$ .

Now, using the recurrence relation,

  $\begin{array}{l}{a}_2=-3a_1=-3(-4)=12\\ a_3=-3a_2=-3(12)=-36\\ a_4=-3a_3=-3(-36)=108\\ a_5=-3a_4=-3(108)=-324\\ a_6=-3a_5=-3(-324)=972\end{array}$

Thus, graph the given sequence by considering $n$ values along the x -axis and their corresponding $a_n$ values along the y -axis. Using the smooth curve to connect the points and, we have