Chapter 3.6, Problem 22PPS

a.

To determine

To determine the function of the arithmetic sequence.

Answer to Problem 22PPS

  $a_n=2n$

Explanation of Solution

Given:

Sequence:

  $2,4,\mathrm{6...}$

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:

The common difference of the arithmetic progression is:

  $4-2=2$

Applying above formula,

  $\Rightarrow a_n=a+(n-1)d$

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

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

Conclusion:

The required function of the sequence is $a_n=2n$ .

b.

To determine

To graph the function.

Answer to Problem 22PPS

  $a_n=2n$

Explanation of Solution

Given:

Sequence:

  $2,4,\mathrm{6...}$

Calculation for graph:

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

First four points are: $(1,2),(2,4),(3,6),(4,8)$

Graph:

  

Interpretation:

From the graph it can be observed that the horizontal extent of the graph is from $-\infty$ to $\infty$ .

And the vertical extent of the graph is also from $-\infty$ to $\infty$ .

So, both the domain and range of the function is $(-\infty ,\infty )$ .

c.

To determine

To determine the domain and range of the function.

Answer to Problem 22PPS

  $D=\{1,2,3,\mathrm{4...}\}\&R=\{2,4,6,8,\mathrm{...}\}$

Explanation of Solution

Given:

Sequence:

  $2,4,\mathrm{6...}$

Calculation / Explanation:

The domain of the function is the number of hours spent at the park.

The range of the function is the number of ridden rides.

So, the domain and range are respectively: $D=\{1,2,3,\mathrm{4...}\}\&R=\{2,4,6,8,\mathrm{...}\}.$

Conclusion:

Therefore, the domain and range are respectively: $D=\{1,2,3,\mathrm{4...}\}\&R=\{2,4,6,8,\mathrm{...}\}.$