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

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Answer 1 · 2016-04-23T20:56:18

$36$

Notice that these are all square numbers:

$4 = 2xx2$

$9 = 3xx3$

$16 = 4xx4$

$25 = 5xx5$

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

$36 = 6xx6$

Another way of writing $axxa$ is $a^2$ .

In general:

$a^n = overbrace(axxaxx...xxa)^"n times"$

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

The first twenty are:

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