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, ?
There is a "Fibonacci" like series is that each digit is the sum of the preceding two numbers: 4 + 8 = 12 8 + 12 = 20 So the series continues: 12 + 20 = 32 20 + 32 = 52 32 + 52 = 84 52 + 84 = 136 and so on. ----------------------------------------------------------------------------- What number do you want to be next? Give me a number and I'll give you a polynomial so that putting in 1, 2, 3, 4 gives the values 4, 8, 12, 20 and putting in 5 gives the number you want.
10
20
4
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.
To find the next number in the sequence 2, -6, 12, 4, 20, we can look for a pattern. The differences between consecutive numbers are -8, 18, -8, and 16, suggesting a pattern of alternating increases and decreases. Following this pattern, the next difference should be -8, so we subtract 8 from 20, giving us 12. Therefore, the next number in the sequence is 12.
56