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
To identify the pattern in the sequence 3, 12, 48, 192, we can observe that each number is multiplied by an increasing factor: 3 × 4 = 12, 12 × 4 = 48, and 48 × 4 = 192. Hence, the pattern involves multiplying each term by 4. To find the next number, we multiply 192 by 4, resulting in 768. Thus, the next number in the sequence is 768.
Pattern: +7,-4,+8,-3,+9,-2... Pattern continuation: +10,-1,+11,*0,+12,+1 17+10=27
The pattern in the sequence 1, 4, 19, 25 can be identified by looking at the differences between consecutive numbers: 4 - 1 = 3, 19 - 4 = 15, and 25 - 19 = 6. The differences themselves (3, 15, 6) do not follow a clear arithmetic or geometric pattern. However, if we analyze the sequence further, the next number could be 36, as it fits a non-linear pattern.
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.