Sequences

A sequence is a function with a domain of positive integers and range of real numbers. In other words, a sequence is a finite or infinite list of real numbers.

There are several types of sequences:

Arithmetic sequences -- common difference
Geometric sequences -- common ratio
Power sequences -- increase by an exponential power
Fibonacci sequences -- no general formula
See-and-say sequences -- visual pattern

Arithmetic sequences

3,5,7,9,11, ...
19,12,5,-2 ,...

12,23,34,45, ...

Geometric sequences

4,8,16,32, ...
75,15,3,3/5, ...
-5, 15, -45, 135, ...

 

Power sequences

1, 4, 9, 16, 25, ...

Fibonacci sequences

1, 1, 2, 3, 5, 8, ...
2, 4, 6, 10, 16, ...

See-and-say sequences

1, 11, 111, 1111, ...
22, 202, 2002, 20002, ...