According to Wittgenstein's Finite Rule Paradox every finite sequence of numbers can be a described in infinitely many ways and so can be continued any of these ways - some simple, some complicated but all equally valid. Conversely, it is possible to find a rule such that any number of your choice can be the next one.
The simplest polynomial rule is
Tn = (103*n4 - 1242*n3 + 5201*n2 - 8670*n +4680)/24 for n = 1, 2, 3, ... and accordingly, the next number is 213.
20
3, -6, 12, 4, 20, ?
To find the next number in the series 4, 8, 12, 20, we need to identify the pattern or rule governing the sequence. In this case, the pattern is that each number is the sum of the previous two numbers. 4 + 8 = 12, 8 + 12 = 20, and 12 + 20 = 32. Therefore, the next number in the series is 32.
4
10
20
10
42
The given pattern appears to alternate between two sequences: one sequence that doubles the previous number (3 to 6 to 12) and another that adds 1 to the previous number (4 to 20). Following this pattern, after 20, the next number in the doubling sequence would be 24, as it continues from 12. Thus, the next number in the pattern is 24.
25 is the next number that appears in that sequence.
56
The answer is: 12.