Question

What is the Fibonacci sequence?

Answer 1

The Fibonacci sequence is the sequence `0, 1, 1, 2, 3, 5, 8,...`, 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 = (sqrt(5)+1)/2 ~~ 1.618034` as `n -> oo`

There are many more interesting properties of this sequence.

See also: http://socratic.org/questions/how-do-i-find-the-n-th-term-of-the-fibonacci-sequence