Chapter 12.2, Problem 9CFU

To determine

To find the common ratio and the next three terms of given geometric sequence.

Answer to Problem 9CFU

Common ratio $=-4$ , next three terms are $-115.2,460.8,-1843.2$ .

Explanation of Solution

Given:

The given geometric sequence is $1.8,-7.2,28.8$ .

Calculation:

Consider $a_1=1.8,a_2=-7.2,a_3=28.8$

Now find the common ratio

  $\begin{array}{l}\frac{a_2}{a_1}=\frac{-7.2}{1.8}=-4\\ \frac{a_3}{a_2}=\frac{28.8}{-7.2}=-4\end{array}$

So, the next three terms are-

  $\begin{array}{l}28.8\times -4=-115.2\\ -115.2\times -4=460.8\\ 460.8\times -4=-1843.2\end{array}$

Therefore the next three terms are $-115.2,460.8,-1843.2$