What is the next 2 numbers in this pattern 7 -28 112 -448?

Answer 1

Any two number that you choose can be next. It is easy to find a rule based on a polynomial of order 5 such that the first four numbers are as listed in the question followed by your chosen numbers in the next two places. There are also non-polynomial solutions. Short of reading the mind of the person who posed the question, there is no way of determining which of the infinitely many solutions is the "correct" one.

With this sequence, for example, the next two numbers could be -2583 and -7168. These are based on the rule:

U(n) = (-875*n^3 + 5775*n^2 - 11410*n + 6552)/6 for n = 1, 2, 3, ...

The above answer is mathematically valid and cannot be faulted. However, I suggest that the answer that is sought is 1792 and -7168.

Answer 2

1792, -7168