It is easy to find a rule based on a polynomial of order 5 such that these numbers are the first five generated by the rule. There are also non-polynomial solutions.
A solution based on a polynomial of order 4 is
Un = (103n4 - 1242n3 + 5201n2 - 8670n + 4680)/24 for n = 1, 2, ..., 5.
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3, -6, 12, 4, 20, 13, 27, 21, 33 -9, +18, -8, +16, -7, +14, -6, +12
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what is the pattern for the following 3, -6, 12, 4, 20
12/20=6/10=3/5 Do you see the pattern?
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.