Chapter 3.6, Problem 4AGP

a.

To determine

To determine the function of the arithmetic sequence.

Answer to Problem 4AGP

  $a_n=1.5n+6.5$

Explanation of Solution

Given:

Sequence:

  $8,9.5,11,\mathrm{12.5...}$

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:

  $\Rightarrow 9.5-8=1.5$

Applying above formula,

  $\Rightarrow a_n=a+(n-1)d$

  $\Rightarrow a_n=8+(n-1)(1.5)$  $[\because a_n=8\&d=1.5]$

  $\begin{array}{l}\Rightarrow a_n=8+1.5n-1.5\\ \Rightarrow a_n=1.5n+6.5\end{array}$

Conclusion:

The required function of the sequence is $a_n=1.5n+6.5$ .

b.

To determine

To graph the function

Answer to Problem 4AGP

  $a_n=1.5n+6.5$

Explanation of Solution

Given:

Sequence:

  $8,9.5,11,\mathrm{12.5...}$

Calculation of Graph:

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

So, first four points are: $(1,8),(2,9.5),(3,11),(4,12.5)$

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 $(-\infty ,\infty )$ .