Given ANY number, it is easy to find a polynomial of order 4 that will generate the above four numbers and the selected fifth.
The simplest polynomial or order 3 that will generate the above numbers is
Un = (-53n3 + 399n2 - 880n + 552)/6 for n = 1, 2, 3, ... and accordingly, the next number is -83.
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The next number in the pattern is 324. Each number in the pattern is obtained by multiplying the previous number by 3.
The next is 3.
It is 43 because 31+12 = 43
It is 15 followed by 6 then 18
3 4 5 6 The next number is 1 plus the previous number So the pattern rule is the next number is n + 1