What is next in sequence 7 21 8 72 9?

Answer 1

According to Wittgenstein's Finite Rule Paradox every finite sequence of numbers can be a described in infinitely many ways and so can be continued any of these ways - some simple, some complicated but all equally valid. Conversely, it is possible to find a rule such that any number of your choice can be the next one.
The simplest polynomial solution is Un = (- 77n4 + 874n3 - 3400n2 + 5321n - 2676)/6 where n = 1, 2, 3, ...and, accordingly, the next term is -693.

Answer 2

What number would you like to be next?

The next number is 42 as the formula for each term is given by:

U{n} = (147n⁵ - 2513n⁴ + 15991n³ - 46675n² + 61562n - 28344)/24