Golden ratio describes the perfectness of nature in ratio. Fibonacci sequence happens in nature in many ways. And Fibonacci Sequence is related to it.
Definition: The nth term is the sum of the previous two terms.
Open/Recursive Form:
F(n+2) = F(n+1) + F(n);
F(n+2) = Sum(F(i), (i:0-n))+1;
F(n)*F(n+1)=Sum(Sq(F(i)), (i:0-n))
Closed Form:
F(n) = (Power(Phi, n) - Power((1-Phi), n))/Sqrt(5) = (Power(Phi, n) - Power((-1/Phi), n))/Sqrt(5)
Golden Ratio, Phi: (1+Sqrt(5))/2