Chapter 6.6, Problem 9E

To determine

To write the first six terms of the sequence then graph the sequence

Answer to Problem 9E

First six terms of the sequence are

  $2,6,18,54,162,486,\mathrm{....}$

Graph of sequence is

  

Explanation of Solution

Given information:

Given $a_1=2,a_n=3a_{n-1}$

Concept used:

To find first six terms put $n=2,3,4,5,6$ successively in $a_n=3a_{n-1}$

As $a_1=2,a_n=3a_{n-1}$

Clearly first term $a_1=2$ is given

Now find other five terms

  $\begin{array}{l}\text{for }n=2,3,4,5,6\text{ successively }\\ a_2=3a_{2-1}=3a_1=3\times 2=6\\ a_3=3a_{3-1}=3a_2=3\times 6=18\\ a_4=3a_{4-1}=3a_3=3\times 18=54\\ a_5=3a_{5-1}=3a_4=3\times 54=162\\ a_6=3a_{6-1}=3a_5=3\times 162=486\end{array}$

Therefore,

First six terms of the sequence are

  $\begin{array}{l}{a}_1=2\\ a_2=6\\ a_3=18\\ a_4=54\\ a_5=162\\ a_6=486\end{array}$

Hence,

Sequence is $2,6,18,54,162,486,\mathrm{....}$

Plot graph of this sequence taking point as $\left(n,a_n\right)$

  

The sequence is a discrete function. So, points on the graph are not connected.