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
The sequence alternates between a number and that number plus one. After 2 comes 3, after 3 comes 12, after 12 comes 13, after 13 comes 52, and after 52 comes 53. Following this pattern, the next number after 53 would be 212, as it follows 52 multiplied by 4 (the previous non-incrementing number). Therefore, the next number in the sequence is 212.
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
The sequence alternates between a number and that number plus one. After 2 comes 3, after 3 comes 12, after 12 comes 13, after 13 comes 52, and after 52 comes 53. Following this pattern, the next number after 53 would be 212, as it follows 52 multiplied by 4 (the previous non-incrementing number). Therefore, the next number in the sequence is 212.
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