**The Fibonacci sequence: {0, 1, 1, 2, 3, 5, 8, 13, 21, …} is a wildly popular topic in the field of mathematics. It is defined recursively in that one adds the two previous entries in order to arrive at the next. These numbers present a variety of interesting properties, a notable one being that the ratio of consecutive entries limits toward the so-called “Golden Mean” (1.6180339…). In this talk we will prove this property by finding the Binet Formula, an explicit rule for the n-th Fibonacci number in the sequence. To do this, we will utilize tools from Linear Algebra.**

**A number of generalizations of the Fibonacci sequence are worth exploration . Time permitting, one such generalization will be discussed. This generalized family of sequences possesses an analogous property where the ratios of consecutive terms also have a limiting value, which leads us to the “Silver Mean”, “Bronze Mean”, “Copper Mean”, etc. **