Chapter 6.6, Problem 8E

To determine

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

Answer to Problem 8E

First six terms of the sequence are

  $10,5,0,-5,-10,-15,\mathrm{....}$

Graph of sequence:

  

Explanation of Solution

Given information:

Given $a_1=10,a_n=a_{n-1}-5$

Concept used:

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

As $a_1=10,a_n=a_{n-1}-5$

Clearly first term $a_1=10$ is given

Now find other five terms

  $\begin{array}{l}\text{for }n=2,3,4,5,6\text{ successively }\\ a_2=a_{2-1}-5=a_1-5=10-5=5\\ a_3=a_{3-1}-5=a_2-5=5-5=0\\ a_4=a_{4-1}-5=a_3-5=0-5=-5\\ a_5=a_{5-1}-5=a_4-5=-5-5=-10\\ a_6=a_{6-1}-5=a_5-5=-10-5=-15\end{array}$

Therefore,

First six terms of the sequence are

  $\begin{array}{l}{a}_1=10\\ a_2=5\\ a_3=0\\ a_4=-5\\ a_5=-10\\ a_6=-15\end{array}$

Hence,

Sequence is $10,5,0,-5,-10,-15,\mathrm{....}$

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.