Chapter 8.1, Problem 22E

(a)

To determine

To write the first five terms of the given sequence using table feature of a graphing utility.

Answer to Problem 22E

Five terms of this sequence are $1,0.70711,0.57735,0.5,0.44721$ respectively.

Explanation of Solution

Given information:

Given sequence

  $a_n=\frac{1}{\sqrt{n}}$

Calculation:

To have the first five terms by graphical utility, firstly click on $Y=$ button of Ti-83 calculator and then write down the provided function of the problem, as shown below:

  

Now, Set the table setup. For this, click on $2^{nd}$ and then click on WINDOW button. After this a new screen appears, In this, set the indpnt as Ask. The screenshot is given below:

  

After this, click on $2^{nd}$ and then click on GRAPH button. After this, a new screen appears. In this, input the degrees to have the required table. The screenshot is given as below:

  

(b)

To determine

To write the first five terms of the given sequence algebraically.

Answer to Problem 22E

Five terms of this sequence are $1,0.70711,0.57735,0.5,0.44721$ respectively.

Explanation of Solution

Calculation:

Given sequence

  $a_n=\frac{1}{\sqrt{n}}$

Value of $n$ begins with1, for five terms of this sequence put $n=1,2,3,4,5$ . So,

  $\begin{array}{c}{a}_1=\frac{1}{\sqrt{1}}\\ =1\\ a_2=\frac{1}{\sqrt{2}}\\ =0.70711\\ a_3=\frac{1}{\sqrt{3}}\\ =0.57735\\ a_4=\frac{1}{\sqrt{4}}\\ =0.5\\ a_5=\frac{1}{\sqrt{5}}\\ =0.44721\end{array}$

Hence, five terms of this sequence are $1,0.70711,0.57735,0.5,0.44721$ respectively. So, it is clear that values obtained from both methods, are same.