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The answer depends on which number is missing. Even if the location of the gap is know, there are infinitely many possible solutions. The solutions listed below are polynomials of the lowest degree.

First:

5 using the rule Un = (-4n3 + 48n2 - 128n + 99)/3

Second:

0 using the rule Un = (-7n3 + 84n2 - 209n + 138)/6

Third:

21.666 (recurring) using the rule Un = (3n3 - 23n2 + 84n - 61)/3

Fourth:

50 using the rule Un = (-11n3 + 90n2 - 121n + 48)/6

Fifth:

65 using the rule Un = (-4n3 + 36n2 - 44n + 15)/3

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Q: What is the missing number in this sequence 1 13 33 53?
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