Chapter 3.6, Problem 8WE

To determine

To find: next two numbers in the given sequence

Answer to Problem 8WE

Next two numbers in the given sequence are $\frac{-1}{4},\frac{1}{8}$

Explanation of Solution

Given information: The sequence is $8,-4,2,-1,\frac{1}{2},\mathrm{...}$

Calculation:

Let the required numbers be x and y

The given sequence is $8,-4,2,-1,\frac{1}{2},x,y$

First find the relation between the given terms in the sequence.

  $\begin{array}{l}-4=\frac{8}{-2}\\ 2=\frac{-4}{-2}\\ -1=\frac{2}{-2}\\ \frac{1}{2}=\frac{-1}{-2}\end{array}$

Now find x and y

  $\begin{array}{l}x=\frac{\frac{1}{2}}{-2}=\frac{-1}{4}\\ y=\frac{x}{-2}=\frac{\frac{-1}{4}}{-2}=\frac{1}{8}\end{array}$

So,

  $x=\frac{-1}{4},y=\frac{1}{8}$