Chapter 3.6, Problem 1BGP

To determine

To find the next term of the series.

Answer to Problem 1BGP

The next term of the series is $64$ .

Explanation of Solution

Given:

Some terms are given as

  $1,4,9,25,\mathrm{...}$

Calculation:

Consider the given terms.

  $1,4,9,25,\mathrm{...}$

In order to evaluate the next term need to know the pattern followed by the series.

  $\begin{array}{l}\begin{array}{l}1=1^2\\ 4=2^2\end{array}\}1+2=3\\ \begin{array}{l}9=3^2\\ 25=5^2\end{array}\}3+5=8\end{array}$

So numbers are

  $\begin{array}{l}1=1^2\\ 4=2^2\\ 9=3^2\\ 25=5^2\\ 64=8^2\\ 1,4,9,25,\mathrm{64...}\end{array}$

Therefore, the next term is $64$ .