Section 9.1: Sequences

A sequence is defined as a function whose domain consists of natural numbers.  

The function values

are the terms of the sequence. 

Finding the Terms of a Sequence

• To find the sequence's recursive formula, look at the first few terms. Then use previous terms to define all other terms

(next = now + 5)

• To find the sequence's explicit formula, look for an apparent pattern. 

Factorials
If n is a positive integer, n factorial is defined by

n! = 1 • 2 • 3 • 4 ... (n - 1) • n

Here are some values of n!:

0! : 1

1! : 1

2!: 1 • 2 • = 2

3!: 1 • 2 • 3 = 6

Common Sequences

Some sequences occur more frequently than others. Some common sequences include:

• Powers of 2: 2, 4, 8, 16...
• Powers of 3: 3, 9, 27, 81...
• Perfect Squares: 1, 4, 9, 16...
• Factorial Numbers: 1, 1, 2, 6, 24...