# What is the Fibonacci sequence?

Oct 4, 2015

The Fibonacci sequence is the sequence $0 , 1 , 1 , 2 , 3 , 5 , 8 , \ldots$, with first terms $0 , 1$ and each subsequent term formed by adding the previous two terms.

#### Explanation:

${F}_{0} = 0$
${F}_{1} = 1$
${F}_{n} = {F}_{n - 2} + {F}_{n - 1}$

The ratio between two consecutive terms tends to the 'Golden ratio' $\phi = \frac{\sqrt{5} + 1}{2} \approx 1.618034$ as $n \to \infty$

There are many more interesting properties of this sequence.