Chapter 7.8, Problem 4STP

For Exercises $1-5,$ choose the correct letter.

What is the next term of the geometric sequence, $-0.3,0.6,-1.2,2.4,\dots .?$

F. -1.2

G. -0.3

H. 2

I. -4.8

To determine

To choose : the next term of the geometric sequence.

F. $-1.2$ G. $-0.3$ H . 2 I. $-4.8$

Answer to Problem 4STP

I. $-4.8$

Explanation of Solution

Given sequence: $-0.3,0.6,-1.2,2.4,\mathrm{.......}$ .

Calculation:

The first term of the sequence is $a_1=-0.3$ .

The common ratio r for a geometric sequence is obtained by dividing any term in the sequence by the previous term.

Therefore, common ratio for given geometric sequence is

  $\begin{array}{l}r=\frac{a_2}{a_1}\\ r=\frac{0.6}{-0.3}=-2\end{array}$

The next term of the sequence is evaluated as

  $\begin{array}{l}{a}_5=a_4\cdot r\\ a_5=2.4\times \left(-2\right)=-4.8\end{array}$

Thus, the next term of the sequence is $-4.8$ .