Chapter 9, Problem 28E

Solution

To find if the sequence $3,3.6,4.32,5.184,\dots$ is geometric or not, and find the common ratio and next two if the sequence is geometric.

The sequence is geometric with common ratio $1.2$ , and the next two terms are $6.2208$ and $\text{7}\text{.46496}$ .

Given information:

The sequence, $3,3.6,4.32,5.184,\dots$ .

Calculation:

Observe the ratio between the terms.

  $\begin{array}{c}\frac{3.6}{3}=1.2\\ \frac{4.32}{3.6}=1.2\\ \frac{4.184}{4.32}=1.2\end{array}$

Since the ratio is same, the sequence is geometric and the common ratio is $r=1.2$ .

Now, find the next two terms by multiplying the common ratio.

  $\begin{array}{c}{a}_5=a_{4}r\\ =4.184\cdot 1.2\\ =6.2208\\ a_6=a_{5}r\\ =6.2208\cdot 1.2\\ =\text{7}\text{.46496}\end{array}$

Conclusion:

The sequence is geometric with common ratio $1.2$ , and the next two terms are $6.2208$ and $\text{7}\text{.46496}$ .