Given any number at all, it is easy to find a polynomial of degree four that will fit the above numbers and the additional one as the first five of the sequence.
A polynomial of degree 3 for the above number is
Un = (2n3 - 11n2 + 23n - 12)/3 for n = 1, 2, ... and accordingly, the next number is 31.
3-6-7-14-15 x2 +1 x2 +1
The next number in the sequence is 15. The pattern is as follows: from 1 to 6 is +5, from 6 to 9 +4, from 9 to 12 +3, from 12 to 14 +2, and then from 14 to the answer (15) +1.
The next number in the sequence would be 30. The general rule is multiply by 2, then add 1. 1 x 2 = 2 2 + 1 = 3 3 x 2 = 6 6 + 1 = 7 7 x 2 = 14 14 + 1 = 15 15 x 2 = 30
4 6 3 6 12 14 11 14
15
14
15
The factors of 6 are 1, 2, 3, and 6The factors of 14 are 1, 2, 7, and 14.
15
24 + 1 + 3 + 6 then repeat so 23 + 1 = 24
14 1/3 minus 6 1/3 equals 8.
15