Composite. It is divisible by 3 for any n.
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4 = -5n + 6n2 if you want to solve for n: 6n2 - 5n - 4 = 0 (3n - 4)(2n + 1) = 0 3n - 4 = 0, n = 4/3 2n + 1 = 0, n = -1/2 n = {-1/2, 4/3}
6(n - 4)(n + 1) n = 4, -1
It could be any number of your choice. Pick a number and I can find you a quartic (power 4) polynomial which will give the above four and your choice as the first five terms. But the simplest cubic rule is Un = (n3 - 6n2 + 8)/3 for n = 1, 2, 3, ... which gives U5 = 5
It can be any number that you like. Given any position (n) and any number in that position Un, it is a simple matter to find a polynomial of degree 5 that will generate the above 5 numbers as the first five and you selection as the nth. In this case there is a much simpler rule: Un = 6n2 + 5 for n = 1, 2, 3, ...
8 (again) The sequence is generated by t(n) = (-n3 + 6n2 + 7n - 12)/6 for n = 1, 2, 3, ...