what comes next in the pattern? 1,4,27, 256,?

Answer 1

1st : 1^1 = 1
2nd : 2^2 = 4
3rd : 3^3 = 27
4th : 4^4 = 256
5th : 5^5 = 3125
6th : 6^6 = 46656
and so on and so forth..

Answer 2

Well, the popular answer is 3125, and they give a function as a reason ( f(x) = x^x, x=1,2,3,etc)

Well my answer is 877, and the function is:

f(x) = 31x^3 - 176x^2 + 314x - 168; which is the polynomial of least degree which fits the data.

f(1) = 1; f(2) = 4; f(3) = 27, f(4) = 256; f(5) = 877

Therefore, there is no definitive solution to the question. There are in fact infinitely many functions which describe the data. Four data points are far too few to jump to conclusions about the nature of patterns.

Let g(x) = (x-1)(x-2)(x-3)(x-4)(N-877) / 24

(note that g(1) = g(2) = g(3) = g(4) = 0, g(5) = N - 877 )

N can be any number you want.

Then the function

h(x) = f(x) + g(x)

will produce:

h(1) = 1, h(2) = 4, h(3) = 27, h(4) = 256, h(5) = N

So the next number in the pattern can be anything you want!!!
The pattern will be described by the function h(x) above.


(I can only conclude that people dont read the other answers when they think they know THE answer, since people keep writing "THE pattern IS n^n..." when I have just given a different pattern which fits the data. They should say " 'A' pattern is n^n.")

Answer 3

This is a sequence of the natural numbers (belonging to the set N without subscript 0) in the power of themselves. 1 to the 1th power is 1, 2^2=4, 3^3=27, 4^4=256, 5^5=3125, 6^6=46656 and so on.

Answer 4

The pattern is 1^1, 2^2, 3^3, 4^4, so the answer is 5^5.
This is equal to 3125

Answer 5

The pattern is n^n. So the next one in the pattern is 5^5=3125.

Answer 6

I got the same answer. 3125 1^1, 2^2 3^3, 4^4, 5^5

Answer 7

3125. It's 1 to the first power, 2 to the second power, 3 to the third power, 4 to the 4th power, 5 to the 5th power.

Answer 8

3125 or 5 to the power of 5

Answer 9

the formula is n^n

1^1 = 1
2^2 = 4
3^3 = 27
4^4 = 256
5^5 = 3125

ANS : 3125

Answer 10

5^5 = 3125