Chapter 3, Problem 21CR

To determine

To predict: the next two numbers in given sequence.

Answer to Problem 21CR

The next two terms of the sequence are $\frac{1}{100}$ and $-\frac{1}{1000}$ .

Explanation of Solution

Given information:

Given sequence is

  $100,-10,1,-\frac{1}{10},\mathrm{...}$

Calculation:

Consider the following sequence:

  $100,-10,1,-\frac{1}{10},\mathrm{...}$

From the above sequence, it can be easily predicted that given next term is divided by $-10$ than the previous term.

First term is 100,

Second term is $-10$ , divide first term is $-10$ .

Third term is 1, divide second term by $-10$ .

Fourth term is $\frac{-1}{10}$ , divide third term by $-10$ .

Fifth term is $\frac{1}{100}$ , divide fourth term by $-10$ .

Sixth term is

  $-\frac{1}{1000}$ , divide fifth term by $-10$ .

And so on.

Hence the next two terms of the sequence are $\frac{1}{100}$ and $-\frac{1}{1000}$ .