Fibonacci and Related Sequences

by **Steven J. Wilson**

You can use this page to investigate the behavior of sequences (and their partial sums) given by the formula

*a*_{n} = *p a*_{n–1} +
*q a*_{n–2}.

The best known sequence of this type is the Fibonacci sequence, which uses the parameters *p* = *q* = 1, and first two terms 1 and 1. The sequence using the same parameters but first terms 1 and 3 is sometimes known as the Lucas sequence.

#### The Graph of the Sequence, Viewed as a Function on the Positive Integers

#### The First Few Terms of the Sequence

t1

#### The Non-Recursive Equation of the Sequence

#### The Sequence Represented as Areas in a Bar Chart

#### The Partial Sums Represented as Areas in a Bar Chart