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

an = p an–1 + q an–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.

Parameter Value, p:
Parameter Value, q:
First Term, a1:
Second Term, a2:
Number of Terms, n:
 

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

an = 

 
 

The Sequence Represented as Areas in a Bar Chart

The Partial Sums Represented as Areas in a Bar Chart