The Fibonacci sequence is the sequence that starts with 0, 1 that increases by the previous two terms added together each time.
In mathematical terms:

F(0) = 0

F(1) = 1

F(x) = F(x-1) + F(x-2)

As the number of terms approaches infinity, the ratio between the last term and the term before that approaches a constant. This is known as the golden ratio. It is approximately equal to 1.61803.

There is another sequence called the Pell Sequence (or the two-bonacci sequence), which is very similar to the Fibonacci sequence:

P(0) = 0

P(1) = 1

P(x) = 2 * P(x-1) + P(x-2)

The ratio between the last two numbers as the length of the sequence approaches infinity also approaches a constant: approximately 2.4142. This is known as the silver ratio.