Chapter 3.6, Problem 24PPS

a.

To determine

To determine the first five terms of the arithmetic sequence.

Answer to Problem 24PPS

  $-3,-1,1,3,5$

Explanation of Solution

Given:

Graph:

  

Calculation:

  $(n,a_n)$ represents the points of the graph.

So, the points on the graph are $(1,-3),(2,-1),(3,1),(4,3),(5,5).$

The terms of the arithmetic sequence are the second coordinate in each coordinate pair.

Conclusion:

The required terms of the arithmetic sequence are $-3,-1,1,3,5$ .

b.

To determine

To determine the formula for the nth term.

Answer to Problem 24PPS

  $a_n=2n-5$

Explanation of Solution

Given:

Graph:

  

Formula used:

nth term of any arithmetic progression is given by the formula:

  $t_n=a+(n-1)d$

  $t_n=$ nth term

  $a=$ The first term of the arithmetic progression

  $d=$ The common difference of the arithmetic progression

Calculation / Explanation:

The common difference of the arithmetic progression is:

  $-1-(-3)=-1+3=2$

Applying above formula,

  $\Rightarrow a_n=a+(n-1)d$

  $\Rightarrow a_n=-3+(n-1)(2)$  $[\because a=-3\&d=2]$

  $\begin{array}{l}\Rightarrow a_n=-3+2n-2\\ \Rightarrow a_n=2n-5\end{array}$

So, the nth term of this sequence is $2n-5.$

Conclusion:

The required nth term formula of the sequence is $a_n=2n-5$ .

c.

To determine

To determine the function

Answer to Problem 24PPS

  $f(n)=2n-5$

Explanation of Solution

Given:

Graph:

  

Calculation:

From the above sub part, the nth term of the sequence is,

  $a_n=2n-5$

So, the function of sequence will be $f(n)=2n-5$ .

Conclusion:

The required function of the sequence is $f(n)=2n-5$ .

d.

To determine

To determine the domain and range of the function

Answer to Problem 24PPS

  $D=\{1,2,3,\mathrm{4...}\}\&R=\{-3,-1,1,3,\mathrm{...}\}$

Explanation of Solution

Given:

Graph:

  

Calculation:

The domain of the function is the numbers of the x -coordinate.

The range of the function is the number of the y -coordinate.

So, the domain and range are: $D=\{1,2,3,\mathrm{4...}\}\&R=\{-3,-1,1,3,\mathrm{...}\}.$

Conclusion:

Therefore, domain and range of the function are $D=\{1,2,3,\mathrm{4...}\}\&R=\{-3,-1,1,3,\mathrm{...}\}$ .