It's true that there are endless "ugly observed" rules to satisfy the series, with arbitrary number fit in the question mark. One of the simplest way to implement your idea is the parameter-selection function build as the following for series C1, C2,... Cm, including the arbitrary answer number put in the question mark:
F(n) = ∑ {i = 1 to m} Ci * ∏{j = 1 to m but j ≠i} [(n-j) /(i-j)]
Thus, F(1) = C1, F(2) = C2, ... F(m) = Cm all holds, and the question mark can be put whatever you want.
Unfortunately, such function cannot be expressed as a simple sentence and looks really ugly for bigger m like 6 or even 8 in our case.
F(n) = ∑ {i = 1 to m} Ci * ∏{j = 1 to m but j ≠i} [(n-j) /(i-j)]
Thus, F(1) = C1, F(2) = C2, ... F(m) = Cm all holds, and the question mark can be put whatever you want.
Unfortunately, such function cannot be expressed as a simple sentence and looks really ugly for bigger m like 6 or even 8 in our case.
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