Chapter 3.6, Problem 1WE

To determine

Predict next two numbers in the sequence.

Answer to Problem 1WE

Sequence with next two numbers is $1,4,16,64,256,1024,\mathrm{...}$

Explanation of Solution

Given:

The given sequence is,

  $1,4,14,64,\mathrm{....}$

Here the given sequence can be written as,

  $\begin{array}{l}1,4,14,64,\mathrm{....}\\ \approx 4^0,4^1,4^2,4^3,\mathrm{....}\end{array}$

As the power of 4 is increasing by 1 in each term.

So, the next two term of the sequence according to the pattern is $4^4{\text{and 4}}^5$ which is equal to

256 and 1024.

So, the sequence will be,

  $1,4,16,64,256,1024,\mathrm{...}$