Chapter 12.1, Problem 24E

a.

To determine

Calculate the first ten terms of the sequence.

Answer to Problem 24E

The first ten terms are: $1,3,2,-1,-3,-2,1,3,2and1.$

Explanation of Solution

Given: It is given in the question that the sequence are $a_n=a_{n-1}-a_{n-2}$ , $a_1=1$ and $a_2=3$ .

Concept Used:

In this, use the concept of putting the values of different number in the sequence n to find the value.

Calculation:

Here, the sequence is $a_n=a_{n-1}-a_{n-2}$ .

Put ,

  $\begin{array}{l}n=3\Rightarrow a_3=a_{3-1}-a_{3-2}=a_2-a_1=3-1=2\\ n=4\Rightarrow a_4=a_{4-1}-a_{4-2}=a_3-a_2=2-3=-1\\ n=5\Rightarrow a_5=a_{5-1}-a_{5-2}=a_4-a_3=-1-2=-3\\ n=6\Rightarrow a_6=a_{6-1}-a_{6-2}=a_5-a_4=-3-(-1)=-2\\ n=7\Rightarrow a_7=a_{7-1}-a_{7-2}=a_6-a_5=-2-(-3)=1\\ n=8\Rightarrow a_8=a_{8-1}-a_{8-2}=a_7-a_6=1-(-2)=3\\ n=9\Rightarrow a_9=a_{9-1}-a_{9-2}=a_8-a_7=3-1=2\\ n=10\Rightarrow a_{10}=a_{10-1}-a_{10-2}=a_9-a_8=2-3=1\end{array}$

Conclusion:

The terms are : $1,3,2,-1,-3,-2,1,3,2and1.$ .

b.

To determine

Draw the graph of the first ten terms .

Explanation of Solution

Given:

It is given in the question that the ten terms are : $1,3,2,-1,-3,-2,1,3,2and1.$ .

Graph:

  

Interpretation:

Here, the above graph will be obtained by putting the value of the ten terms are : $1,3,2,-1,-3,-2,1,3,2and1.$ , In the graphing calculator to get the required graph.