Chapter 4.7, Problem 2LC

To determine

To find: The pattern of the sequence $3,-6,12,-24,\dots$ and the next two terms.

Answer to Problem 2LC

The pattern of the sequence $3,-6,12,-24,\dots$ is geometric progression and the next two terms are 48 and $-96$ .

Explanation of Solution

Given:

The sequence is $3,-6,12,-24,\dots$ .

Calculation:

Divide the second term with the first term to obtain the ratio as,

  $\frac{-6}{3}=-2$

Divide the third term with the second term to obtain the ratio as,

  $\frac{12}{-6}=-2$

Divide the fourth term with the third term to obtain the ratio as,

  $\frac{-24}{12}=-2$

Since the ratio is same, therefore, the sequence is geometric progression.

The next two terms of GP is calculated as follows:

  $\begin{array}{c}-24\times \left(-2\right)=48\\ 48\times \left(-2\right)=-96\end{array}$

Thus, the pattern of the sequence $3,-6,12,-24,\dots$ is geometric progression and the next two terms are 48 and $-96$ .