Series

Series is the sum of the elements of the Sequence. For example $2,4,6,8$ is a sequence with four elements and the corresponding series will be $2+4+6+8$ where the sum of the series or value of the series will be 20.

Difference Between Sequence and Series

Sequence	Series
In sequence, elements are placed in a particular order following a particular set of rules.	In series, the order of the elements is not necessary.
It is just a collection (set) of elements that follow a pattern.	It is a sum of elements that follow a pattern.
Order of appearance of the numbers is important.	The order of appearance is not important.
Example: Arithmetic Sequence $1,3,5,7,9,11,13,15$	Example: Arithmetic Series $1+3+5+7+9+11+13+15$

Types of Series

Arithmetic Series

An Arithmetic Series is a series formed by using an arithmetic sequence. for example $1+3+5+7+9+11+13+15$ is an arithmetic series.

Geometric Series

A geometric Series is a sequence where every term bears a constant ratio to its preceding term. This ratio is called the "common ratio". The terms of the geometric sequence are of the form $a,ar,ar^{2},......$

Example: $1,4,16,64,.......$ Here $a=1,d=4$

Fibonacci Series

Fibonacci Series is a sequence where every term is the sum of the last two preceding terms.

Example:

$0,1,1,2,3,5,8,13,21,34$