How do you get each number in the Fibonacci sequence?

Answer 1

The Fibonacci sequence is a series of sums of two counting numbers and it starts with the lowest two, namely 0 and 1. Each successive number in the sequence is the sum of the two preceding it. Like this:

The first term is usually 0 (although sometimes it is left out).

The second term is 1.

The third term is 1 + 0 = 1.

The fourth term is 1 + 1 = 2.

The fifth term is 1 + 2 = 3.

The sixth term is 2 + 3 = 5.

So the first 15 terms in the sequence would be:

0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, 377, ...

More formally, the Fibonacci sequence is defined recursively as:

a1 = 0

a2 = 1

an+1 = an-1 + an

There is also a general formula for the nth Fibonacci number:

( [1+sqrt(5)]n - [1-sqrt(5)]n ) / (2n * sqrt(5))

(where sqrt() means square root of)