sequence and series

A sequence is an ordered list of numbers or terms. It can contain elements, numbers and terms and can be a limited set or an infinite set. A series on the other hand is the sum of a sequence. 

Sequences can be finite or infinite, such as the sequence of all even positive integers (2, 4, 6...). Finite sequences are sometimes known as strings or words and infinite sequences as streams. The empty sequence ( ) is included in most notions of sequence, but may be excluded depending on the context. The sequence can also be in accessing order or descending order. It usually follows a pattern which can easily be figured out. A sequence may be named or referred to as "A" or "A n ". The terms of a sequence are commonly named as something like "ai" or "an", with the subscripted letter "i" or "n" being the "index" or counter. Example: A2 is  the second place  in the sequence will A6 denotes the six place in the sequence

A series on the other hand is the summation of a sequence.  It is indicated with a either the Latin capital letter "S" or  the Greek letter  that corresponds to S, known as Sigma ‘∑”. It is usually the sum of a set sequence.For example the summation of the first through tenth terms of a sequence