What is the formula for 128 64 32 16 8 4 2?

Answer 1

There is no unique formula. Given a set of any 7 numbers it is always possible to find a polynomial of order 6 that will generate those numbers as the first set of numbers. For example,

Un = (n6 - 33n5 + 475n4 - 3915n3 + 20044n2 - 61932n + 91440)/360

for n = 1, 2, ... , 7 will give the above 7 numbers.

You need to be able to second-guess what the questioner had in mind. In this case you may notice that each number is half the previous one. So the expected answer is

Un = 28-n.

Mathematically, both answers are correct but unfortunately, in most cases the first will not be accepted.