# What is the next number in the pattern: 4, 9, 16, 25?

Apr 23, 2016

$36$

#### Explanation:

Notice that these are all square numbers:

$4 = 2 \times 2$

$9 = 3 \times 3$

$16 = 4 \times 4$

$25 = 5 \times 5$

So we would expect the next number in the sequence to be:

$36 = 6 \times 6$

Another way of writing $a \times a$ is ${a}^{2}$.

In general:

${a}^{n} = {\overbrace{a \times a \times \ldots \times a}}^{\text{n times}}$

You will find that it is very useful to know a few square numbers.

The first twenty are:

$1 , 4 , 9 , 16 , 25 , 36 , 49 , 64 , 81 , 100 , 121 , 144 , 169 , 196 , 225 , 256 , 289 , 324 , 361 , 400$