Given any number, it is possible to find a polynomial of degree 5 that will generate the above sequence of numbers and the additional sixth. There are also non-polynomial rules possible.
The polynomial of degree 4 that will generate this sequence is
Un = (103n4 - 1242n3 + 5201n2 - 8670n + 4680)/24 for n = 1, 2, 3, ... and, according to this rule, the next number is 213.
20/12 = 5/3 = 12/3
20/12 = 18/12 = 12/3
The sequence changes by multiplying with different numbers: from 3 to -6 (* -2), -6 to 12 (* -2), 12 to 4 (* 0.33), and 4 to 20 (* 5). If we continue this pattern, 20 multiplied by 0.5 gives us 10. So, the next number is 10.
20 over 12 s a mixed number = 12/3
3, -6, 12, 4, 20, ?
20/12 = 5/3 = 12/3
20/12 = 18/12 = 12/3
The sequence changes by multiplying with different numbers: from 3 to -6 (* -2), -6 to 12 (* -2), 12 to 4 (* 0.33), and 4 to 20 (* 5). If we continue this pattern, 20 multiplied by 0.5 gives us 10. So, the next number is 10.
20 over 12 s a mixed number = 12/3
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
48
12
65 (each jump is 3, 6, 9, 12, 15, 18, etc)
12
36
3