What is the next number in the series 1 4 9?

Answer 1

It depends on what you would like it to be. You can select a rule so that any number can be next. For example, if you select the rule:

• Un = (-8*n^3 + 51*n^2 - 88*n + 48)/3, then the next number is 0;
  
• Un = (-5*n^3 + 32*n^2 - 55*n + 30)/2, then the next number is 1;
  
• Un = (-7*n^3 + 45*n^2 - 77*n + 42)/3, then the next number is 2;

and so on. Furthermore, the next number need not be an integer.

So the question should be "what is your best guess as to the rule that the questioner had in mind for the first three numbers and, if that guess is correct, what is the next number?"

The answer to that question is 16.

Answer 2

16