The Fibonacci Numbers have been of great interest since they were first seen as a solution to an algebra word problem published in 1202. The Fibonacci Numbers have many interesting properties which have many applications. For this the focus will be on finding a formula to find the nth Fibonacci number in the sequence.
The sequence is set up so that –
For any integer value of n 0 or greater.
This is called the renewal equation. It uses information from the current and previous steps to generate future steps. It is also a second order difference equation.
This is for 0 or greater integer values of n=0,1,2,3…
This is a system of irrational numbers that always answers with an integer.
Also $$\lambda_1\approx 1.6180339887…$$ is the value known as the Golden Section or Golden Ratio.