The Fibonacci sequence begins with a chosen pair of starting values, with each later value formed by adding the previous two. It is a simple problem that teaches loops, recursion, generators, memoization, and algorithmic complexity.
An iterative solution is usually the clearest and most efficient for generating a sequence in order. A basic recursive solution mirrors the mathematical definition but repeats the same calculations and becomes slow quickly. Memoization stores earlier results, while a generator produces values one at a time without keeping the entire sequence in memory.
For very large indexes, specialized mathematical methods can reduce the number of operations, but they also make the code harder to explain. Validate inputs, define whether the requested count or maximum value controls the output, and test edge cases. The most useful lesson is not the sequence itself; it is how algorithm choice changes performance.