The Fibonacci series is a famous mathematical sequence where each number is the sum of the two preceding numbers. Starting with 0 and 1, we get 0, 1, 1, 2, 3, 5, 8, 13, 21, and so on. The mathematical formula is F(n) equals F(n-1) plus F(n-2), with base cases F(0) equals 0 and F(1) equals 1. This simple rule creates a sequence with fascinating mathematical properties.
The iterative approach uses three variables to efficiently generate Fibonacci numbers. We start with previous equals zero and current equals one. For each step, we calculate next as the sum of previous and current, then update our variables: previous becomes current, and current becomes next. This table shows how the variables change through the first eight Fibonacci numbers, demonstrating the systematic progression of the iterative method.