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#