Chapter 11.1, Problem 14CYU

To determine

To find out the next three terms of geometric sequence and then graph the sequence.

Answer to Problem 14CYU

The next three terms are 40.5 , 60.75 , 91.125

Explanation of Solution

Given: 8 , 12 , 18 , 27 ,....

Formula used;

  

where r is the common ratio

  

Calculation:

  $\begin{array}{l}{a}_1=8\\ a_2=12\\ a_3=18\\ a_4=27\\ \\ r=\frac{a_2}{a_1}=\frac{12}{8}=1.5\\ a_n=a{r}^{n-1}\\ a_5=a{r}^4\\ $ =8{(1.5)}^4$=40.5\\ \\ a_6=a{r}^5\\ $ =8{(1.5)}^5$=60.75\\ \\ a_7=a{r}^6\\ $ =8{(1.5)}^6$=91.125\end{array}$

GRAPH:

  

INTERORETATION:

According to graph , geometric sequence is increasing in every step.