The FAST method is built around the idea of taking a brute force solution and making it dynamic. Therefore the first step is to find that brute force solution. In the case of finding the nth fibonacci number, we can just write a simple recursive function:
Dynamic programming. The last resort of any interviewer set on seeing you fail. Your interview has gone great up until this point, but now it grinds to a standstill. Somewhere in the back of your mind you remember something about arrays and memoization, but the memory is hazy at best. You fumble, you trip, you drop the ball. Game over.