The missing number in the series 1, 4, 27,____, 3125 is?

The missing number in the sequence is 256. This is because the numbers are determined by the formula n^n (n to the power of n). The pattern is as follows:

- 1^1 = 1
- 2^2  (2x2) = 4
- 3^3 (3x3x3) = 27
- 4^4 (4x4x4x4) = 256
- 5^5 (5x5x5x5x5) = 3125

It is known as a sequence of integer to the second tetration. To find the answer you have to determine the relationship of each number to its numerical place in order. Since the missing number would be the fourth number would be the fourth number in the sequence, this means that n=4.

Therefore the answer is found by finding out 4^4

- 4x4 = 16
- 4x4x4 = 64
- 4x4x4x4 = 256

The term 'tetration' was coined by the English mathematician Reuben Louis Goodstein. For a more in depth explanation and definition of what tetration is and how it can be applied, then you can check the following Wikipedia page - en.wikipedia.org/wiki/Tetration

If you are looking for more number puzzles to try out in order to test yourself, then there are plenty of websites that you could look at. Examples include:

- brainden.com/number-puzzles.htm
- oeis.org/Spuzzle.htm
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