The Fibonacci sequence is a series of numbers where each number is the sum of the two preceding ones, usually starting with 0 and 1.

The Recurrence Relation:

$$ F_n = F_{n-1} + F_{n-2} $$

with seed values $F_0 = 0$ and $F_1 = 1$.

The Golden Ratio (φ):

As the sequence progresses, the ratio of consecutive Fibonacci numbers ($F_n / F_{n-1}$) approaches the Golden Ratio, which is approximately 1.618.

$$ \lim_{n\to\infty} \frac{F_n}{F_{n-1}} = \phi = \frac{1+\sqrt{5}}{2} \approx 1.6180339... $$