2n + 8 = -142n = -22n = -11
Given any 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 and the next is the given number. There are also non-polynomial solutions.The simplest polynomial solution, of order 4, isUn = (-n4 + 10n3 - 11n2 - 142n + 456)/24 for n = 1, 2, 3, ...and accordingly, the next in the sequence is U6 = 3.
2n + 8 = -142n = -22n = -11
Given any 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 and the next is the given number. There are also non-polynomial solutions.The simplest polynomial solution, of order 4, isUn = (-n4 + 10n3 - 11n2 - 142n + 456)/24 for n = 1, 2, 3, ...and accordingly, the next in the sequence is U6 = 3.