Chapter 9, Problem 5RE

To determine

To draw a graph of the sequence with given nth term

Answer to Problem 5RE

  

Explanation of Solution

Given information : 

  $a_n=\frac{2^{n+1}+{\left(-1\right)}^n}{2^n},n=1,2,3,\mathrm{......}$

Concept used:

Some graphing calculators have a built-in sequence graphing mode that makes it easy to graph sequences defined recursively. The function names used in this mode are u, v, and w.

This procedure will be used to graph the sequence of given equation.

Explanation: 

  $Let{\text{ X}}_{1T}=T,Y_{1T}=\frac{{\left(2\right)}^{T+1}+{\left(-1\right)}^T}{2^T}$

x	y
1	$\frac{3}{2}$
2	$\frac{9}{4}$
3	$\frac{15}{8}$
4	$\frac{33}{16}$
5	$\frac{63}{32}$
6	$\frac{129}{64}$
7	$\frac{255}{128}$
8	$\frac{513}{256}$
9	$\frac{1025}{512}$
10	$\frac{2049}{1024}$
11	$\frac{4095}{2046}$
12	$\frac{8193}{4096}$
13	$\frac{16385}{8192}$
14	$\frac{32769}{16384}$
15	$\frac{65535}{32768}$
16	$\frac{131073}{65536}$
17	$\frac{262143}{131072}$
18	$\frac{524289}{262144}$
19	$\frac{1048575}{524288}$
20	$\frac{2097153}{1048576}$

Using these coordinates plotting the graph

  

Set Tmin =1, Tmax=20 and Tstep=1. Even though the domain of the sequence is all positive integers, choose value of for Tmax to use parametric graphing mode. Finally choose Xmax=20, Xmin=0, Xscl=2, Ymin=0, Ymax=3, Yscl=1, and draw the graph.