Upon teaching one-on-one students of various subjects, this led to eventually summarize the concept of solving the reccurence relation that makes the Fibonacci Sequence in 3 different ways, each connecting to the solution that involves the Golden Ratio.
We motivate the Golden Ratio, then cover a Differential Equation type solve using Superposition, solve it again with Linear Algebra, then solve it again a third time using Generating Functions from Discrete Math.