Skippy the Duck moves on a one-dimensional axis his whole life. He starts at point a, and makes a b-point skip every day, but you don't know in which direction. This means, day 2 he's either at a-b or a+b, an day 3, he's either at a-2b or at a+2b (the sign of the skip remains the same).
Cruel that it is, you'd like to shoot and kill skippy. Problem is, you're blind-folded (you can't observe skippy's location or moves), and your gun will fire only once a day. However, you're such a skilled sniper that you can pick any point you'd like, and shoot. Assuming you're immortal, find a strategy so that you'll kill skippy.
Mathematically speaking, find f(n) such that for every a, b, there exists n s.t. f(n) = a + bn
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