What comes next in this pattern 3 -6 12 4 20?

Answer 1

13

Starting with the number three, the pattern appears to be :-

Subtract 9 then add 2 x 9 which generates -6, 12

Subtract 8 then add 2 x 8 which generates 4, 20

So the next steps are, subtract 7 then add 2 x 7 to produce 13, 27.

Answer 2

Any number that you choose can be the next number. It is easy to find a rule based on a polynomial of order 5 such that the first five numbers are as listed in the question followed by the chosen next number. There are also non-polynomial solutions. Short of reading the mind of the person who posed the question, there is no way of determining which of the infinitely many solutions is the "correct" one.The given sequence can be generated using the following polynomial of order 4:U(n) = (103*n^4 - 1242*n^3 + 5201*n^2 - 8670*n + 4680)/24 for n= 1, 2, 3, ...and, accordingly, the next term is 213.