Chapter 3.6, Problem 5CYU

To determine

To determine the equation and the graph of the given sequence.

Answer to Problem 5CYU

  $a_n=17-2n$

Explanation of Solution

Given:

Sequence:

  $15,13,11,\mathrm{9...}$

Calculation:

The common difference of the arithmetic progression is:

  $13-15=-2$

Applying above formula,

  $\Rightarrow a_n=a+(n-1)d$

  $\Rightarrow a_n=15+(n-1)(-2)$  $[\because a=15,d=-2]$

  $\begin{array}{l}\Rightarrow a_n=15-2n+2\\ \Rightarrow a_n=17-2n\end{array}$

Calculation for graph:

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

First four points are: $(1,15),(2,13),(3,11),(4,9)$

To find 5^th point substitute n = 5 in nth term.

  $\begin{array}{c}{a}_n=-2n+17\\ =-2(5)+17\\ =-10+17\\ =7\end{array}$

So, the fifth point: $(5,7)$

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 $(-\infty ,\infty )$ .