Chapter 8, Problem 40CR

(a)

To determine

To find: The missing term of the geometric sequence by the table feature of the graphing utility.

Answer to Problem 40CR

Theninth term of the sequence is $1.29\times {10}^{-4}$ .

Explanation of Solution

Given:

The third term is $a_3=6$ , and fourth term $a_4=1$ .

Calculation:

Use T183 calculator to find the ninth term of the sequence.

The first step is to press the 2^nd and STAT button to access the list menu. Highlight the OPS column and then press 5.

The display is shown in Figure 1

  

Figure 1

The second step is to write the sequence followed by the variable name and then the corresponding limits and then press the enter button as shown in Figure 2

  

Figure 2

The third step is to use the arrow key to get the ninth term as shown in Figure 3

  

Figure 3

From above it clear that the ninth term of the sequence is $1.29\times {10}^{-4}$ .

(b)

To determine

To find: The missing term of the geometric sequence by algebraically.

Answer to Problem 40CR

The value of the 9^th term is $1.29\times {10}^{-4}$ .

Explanation of Solution

Given:

The third term is $a_3=6$ , and fourth term $a_4=1$ .

Calculation:

Consider the common ratioof the geometric sequence is,

  $\begin{array}{c}r=\frac{a_4}{a_3}\\ =\frac{1}{6}\end{array}$

The formula for the nth term of the geometric sequence is,

  $a_n=a\times r^{n-1}$

Then, the ninth term of the sequence is,

  $\begin{array}{c}{a}_n=a_3\times {\left(\frac{1}{6}\right)}^{7-1}\\ =6{\left(\frac{1}{6}\right)}^6\\ =\frac{1}{7776}\\ =1.29\times {10}^{-4}\end{array}$