Extension: Fibonacci Sequence - Expii

The Fibonacci sequence goes 1, 1, 2, 3, 5, 8, 13, 21, ..., starting with 1, 1 (at positions 1 and 2) and then, at each step, adding the previous two terms to get the next Fibonacci number. Fibonacci numbers appear surprisingly often in nature, and they're closely related to the famous "golden ratio" φ = (1+√5)/2 = 1.618... (itself a popular player in architecture).