Chapter 4.7, Problem 10PPE

To determine

To find: The pattern of the sequence $8,4,2,1,\dots$ and the next two terms.

Answer to Problem 10PPE

The pattern of the sequence $8,4,2,1,\dots$ is geometric progression and the next two terms are $\frac{1}{2}$ and $\frac{1}{4}$ .

Explanation of Solution

Given:

The sequence is $8,4,2,1,\dots$ .

Calculation:

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

  $\frac{4}{8}=\frac{1}{2}$

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

  $\frac{2}{4}=\frac{1}{2}$

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

  $\frac{1}{2}$

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

The next two terms of GP is calculated as follows:

  $\begin{array}{c}1\times \left(\frac{1}{2}\right)=\frac{1}{2}\\ \frac{1}{2}\times \left(\frac{1}{2}\right)=\frac{1}{4}\end{array}$

Thus, the pattern of the sequence $8,4,2,1,\dots$ is geometric progression and the next two terms are $\frac{1}{2}$ and $\frac{1}{4}$ .