Difference Between Sequence and Series

The key difference between sequence and series, Sequences are lists of numbers or other mathematical objects that follow a particular pattern or rule. And series is the sum of the terms in a sequence.

In this article we will discuss the difference between sequence and series along with separate discussion on both of them.

Sequence

A sequence is a list of numbers or other mathematical objects that follow a particular pattern or rule. Each object in the list is called a term.

Example

• The sequence of even numbers (2, 4, 6, 8, 10, …) is a list of numbers that follow the rule “add 2 to the previous term to get the next term.”
• The sequence of even numbers (2, 4, 6, 8, …) follows the rule that each term is 2 more than the previous term.

Series

A series is the sum of the terms in a sequence.

Example

• The series 2 + 4 + 6 + 8 + … is the sum of the terms in the even number sequence.
• The series 2 + 4 + 6 + 8 + … is the sum of the terms in the even number sequence.

Sequence vs Series

The differences between sequence and series are given below:

Sequence	Series
It pertains to the arrangement of terms in a specific order.	Sum of the terms in a sequence
Ordering of elements is significant	Order of elements is not important
Follows a specific pattern or rule	Represents the sum of those terms
Example: 1, 2, 4, 8, 16, …	Example: 1 + 2 + 4 + 8 + 16 + …
Can be finite or infinite	Can be finite or infinite
Represented by an ellipsis or a formula	Represented by a mathematical expression using summation notation, such as Σn=1∞an
They do not have any mathematical symbols associated with them	They are represented using the plus (+) symbol to indicate the summation of the terms.