Chapter 8.1, Problem 20E

(a)

To determine

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

Answer to Problem 20E

Five terms of this sequence are $0.75,0.5625,0.42188,0.31641,0.2373$ respectively.

Explanation of Solution

Given information:

Given sequence

  $a_n=\frac{3^n}{4^n}$

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 20E

Five terms of this sequence are $0.75,0.5625,0.42188,0.31641,0.2373$ respectively.

Explanation of Solution

Calculation:

Given sequence

  $a_n=\frac{3^n}{4^n}$

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

  $\begin{array}{c}{a}_1=\frac{3^1}{4^1}\\ =0.75\\ a_2=\frac{3^2}{4^2}\\ =\frac{9}{16}\\ =0.5625\\ a_3=\frac{3^3}{4^3}\\ =\frac{27}{64}\\ =0.42188\\ a_4=\frac{3^4}{4^4}\\ =\frac{81}{256}\\ =0.31641\\ a_5=\frac{3^5}{4^5}\\ =\frac{243}{1024}\\ =0.2373\end{array}$

Hence, five terms of this sequence are $0.75,0.5625,0.42188,0.31641,0.2373$ respectively. So, it is clear that values obtained from both methods, are same.