Fibonacci Sequence

The sequence 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, ... is called the Fibonacci sequence. The first and second terms are both equal to 1, and each term thereafter is the sum of the previous two terms.

The Fibonacci sequence and the sequence obtained by listing the quotients of successive terms are both displayed.

Use the arrow buttons to move through the sequence. For larger and larger values of n, compare the quotient

with the Golden Ratio,

which in decimal form is equal to 1.618033988...

Repeat this exercise with other sequences, using whole-number values other than 1,1 for the initial terms defining the sequence.