It is easy to find a rule based on a polynomial of order 5 such that these numbers are the first five generated by the rule. There are also non-polynomial solutions.
A solution based on a polynomial of order 4 is
Un = (103n4 - 1242n3 + 5201n2 - 8670n + 4680)/24 for n = 1, 2, ..., 5.
3, -6, 12, 4, 20, 13, 27, 21, 33 -9, +18, -8, +16, -7, +14, -6, +12
what is the pattern for the following 3, -6, 12, 4, 20
14
12/20=6/10=3/5 Do you see the pattern?
768
20/12 = 5/3 = 12/3
3, -6, 12, 4, 20, 13, 27, 21, 33 -9, +18, -8, +16, -7, +14, -6, +12
20/12 = 18/12 = 12/3
20 over 12 s a mixed number = 12/3
what is the pattern for the following 3, -6, 12, 4, 20
14
12/20=6/10=3/5 Do you see the pattern?
3, -6, 12, 4, 20, ?
20/12 can not be expressed as a whole number but as a mixed number it is 1 and 2/3
12
768
3/5 of 20 = 1220 / 5 = 44 x 3 = 123/5 of 20 is 12. This is because 3/5*20/1=60/5 which reduces to 12.