Chapter 9.2, Problem 33E

To determine

The next three numbers in the given pattern

Answer to Problem 33E

  $\sqrt{18},2\sqrt{5},\sqrt{22}$

Explanation of Solution

Given:

The given pattern is

  $\sqrt{2},2,\sqrt{6},2\sqrt{2},\sqrt{10},2\sqrt{3},\sqrt{14},4,\mathrm{...}$

Calculation:

Look at all the odd terms in the given pattern:

  $\sqrt{2},\sqrt{6},\sqrt{10},\sqrt{14}$

These are increasing by +4, therefore the next terms in this series for odd places will be:

  $\sqrt{18},\sqrt{22},\sqrt{26}\mathrm{....}$

Now, look at even terms in the given pattern:

  $\begin{array}{l}2,2\sqrt{2},2\sqrt{3},4\\ =2\sqrt{1},2\sqrt{2},2\sqrt{3},2\sqrt{4}\end{array}$

Looking at these terms, the next terms in this series for even places will be:

  $2\sqrt{5},2\sqrt{6}\mathrm{.....}$

Therefore, the next three terms in the given pattern will be:

  $\sqrt{18},2\sqrt{5},\sqrt{22}$