Chapter 12.2, Problem 8E

a.

To determine

Calculate the first five terms of the sequence.

Answer to Problem 8E

The first five term of the sequence are $0,\frac{1}{2},1,\frac{3}{2},2$ .

Explanation of Solution

Given:

It is given in the question that the sequence is $a_n=\frac{1}{2}(n-1)$ .

Concept Used:

In this, use the concept of putting the value of counting numbers in the sequence to get the answer.

Calculation: Here, the sequence is $a_n=\frac{1}{2}(n-1)$ .

Put, $n=1,2,3,4,5$

  $\begin{array}{l}{a}_n=\frac{1}{2}(n-1)nthterm\\ a_1=\frac{1}{2}(1-1)=0;n=1\\ a_2=\frac{1}{2}(2-1)=\frac{1}{2};n=2\\ a_3=\frac{1}{2}(3-1)=1;n=3\\ a_4=\frac{1}{2}(4-1)=\frac{3}{2};n=4\\ a_5=\frac{1}{2}(5-1)=2;n=5\end{array}$

Conclusion:

The first five term of the sequence are $0,\frac{1}{2},1,\frac{3}{2},2$ .

b.

To determine

Find the common difference ( d ).

Answer to Problem 8E

The common difference is $\frac{1}{2}$ .

Explanation of Solution

Given:

It is given in the question that the terms are $0,\frac{1}{2},1,\frac{3}{2},2$ .

Concept Used:

In this, use the concept of arithmetic progression with formula $d=a_2-a_1$ .

Calculation: Here, the term are $0,\frac{1}{2},1,\frac{3}{2},2$ .

  $\begin{array}{l}d=a_2-a_1\\ d=\frac{1}{2}-0\\ d=\frac{1}{2}\end{array}$

Conclusion:

The common difference is $\frac{1}{2}$ .

c.

To determine

Draw the graph of the terms.

Explanation of Solution

Given:

It is given in the question that the term are $0,\frac{1}{2},1,\frac{3}{2},2$ .

Graph:

  

Interpretation:

Here, put all the terms $0,\frac{1}{2},1,\frac{3}{2},2$ in the TI − eighty three calculator and it gives us the required graph as shown above with correct point.