A Sequence is a list of numbers connected by a rule.

A Series is the sum of a sequence

There are two main types of series:

Arithmetic Progressions and Geometric Progressions.

Arithmetic Progressions have a common difference between each term.

n^th term = a + (n - 1)d, where a = first term, and d = common difference.

The sum of the first n terms is:

, pairs each totalling (a + l) - (the sum of the first and last terms.)

This can be rewritten using the formula for the n^th term to get:

Geometric Progressions have a common ratio (multiple) between each term.

n^th term = ar^n-1 , where a = first term, and r = common ratio

The sum of the first n terms is:

or

This is the sum to infinity and this sum only converges when:

The Arithmetic mean of two numbers (m and n) =

The Geometric mean of two numbers =