There are many posible answers. One of them is
Un = (-n4 + 13n3 - 53n2 + 95n - 36)/6 for n = 1, 2, 3, ...
There is no pattern
The sequence appears to alternate between adding and subtracting numbers. The pattern seems to be +11, -7, +5, -2, +6. Following this pattern, the next number in the sequence would be +3 from the previous number, which would be 21.
13 20 12
Pattern: +7,-4,+8,-3,+9,-2... Pattern continuation: +10,-1,+11,*0,+12,+1 17+10=27
The sequence reflects a pattern of multiplying by 3, then adding 3, to each successive value. The next value would be 144. Explanation: 4x3=12, 12+3=15, 15x3=45, 45+3=48, 48x3=144
3, -6, 12, 4, 20, 13, 27, 21, 33 -9, +18, -8, +16, -7, +14, -6, +12
3/19 : 12/19 : 4/19
If one may choose the break points, it looks like simple doubling: 3 - 6 - 12 - 24
21 and 13. The pattern is t(n) = (-n4 + 10n3 - 23n2 + 38n - 12)/12
The pattern seems to be +1 +3 +1 +3 (3+1 = 4, 4+3 = 7, 7+1 = 8, etc...) So next in the sequence would be 12.
The pattern in the sequence 11 12 14 17 21 is an increasing sequence where each number is the sum of the previous number and a specific value. In this case, the specific value is increasing by 1 with each subsequent number. So, starting from 11, we add 1 to get 12, then add 2 to get 14, add 3 to get 17, and add 4 to get 21.
Each number is decreasing by 3. The next numbers in the sequence would be -18, -21, -24, -27, -30.