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What is the rule to this pattern 1 6 21 56 126?
t(n) = (5n4 - 10n3 + 55n2 - 50n + 24)/24 where n = 1, 2, 3, ...
What comes next 1 2 0 3 -1?
It depends on what number you would like. Given any real number, it is possible to find a real polynomial of degree 5 that will go through these 5 and the nominated 6th number. Fitting a polynomial of degree 4 to these numbers, the fitted next number is 44. Un = (-5n4 + 58n3 - 232n2 + 371n - 186)/6 for n = 1, 2, 3, ... ------------------------ All the above is true but just in case the simple answer is the real answer, I'd bet on 4 (then -2, 5,-3)
What is the nth term for 5 14 23 32?
It could be Un = (-3n4 + 30n3 - 105n2 + 168n - 80)/2 or Un = (-5n4 + 50n3 - 175n2 + 286n - 136)/4 or any one of infinitely more polynomials of order >1, or other types of functions. The simplest polynomial solution is Un = 9n - 4 or any
