Which number best completes the sequence 1 5 16 31 51?

Answer 1

81 is a good continuation although, since the seqeunce continues forever, it cannot be said to be completion.

The rationale for 81 is

u(n) = (n4 - 13n3 + 74n2 - 122n + 66)/6 for n = 1 ,2, 3, ...