Difference Between Sequence and Series

Sequence and Series is one of the important topics in Mathematics. Though many students tend to get confused between the two, these two can be easily differentiated. Sequence and series can be differentiation as the order of sequence always matter but it’s not the case with series.

Difference between Sequence and Series

Sequence Series
Sequence relates to organization of terms in a particular order (i.e. related terms follow each other) and series is the summation of the elements of a sequence. Series can also be classified as a finite and infinite series.
Example: 1, 2, 4, 6, 8, . . . . n are said to be in a Sequence and 1 + 2 + 4 + 6 + 8 . . . . n is said to be in a series. A finite series can be represented as m1 + m2 + m3 + m4 + m5 + m6 + . . . . . + mn
In a sequence every term is related to the succeeding and preceding term. It can be classified into finite sequence or infinite sequence. A sequence like p1, p2, p3, p4, p5, p6, . . . . . . , pn, is known as a Finite Sequence. an Infinite series can be written as m1 + m2 + m3 + m4 + m5 + m6 + . . . . . + mn + . . . . .
General Form: \([p_{i}]_{i=1}^{n}\). Unending sequence like p1, p2, p3, p4, p5, p6, . . . . , pn, . . . . . , is known as an infinite sequence. If m1 + m2 + m3 + m4 + m5 + m6 + . . . . . . + mn = Sn, then Sn is termed as the sum to n elements of the series. 
General Form: \([p_{n}]_{n=1}^{\infty }\). General Form: \(S_{n}=\sum_{r=1}^{n}m_{r}\). 
The order of a sequence matters. Hence, a sequence 5, 6, 7 is different from 7, 6, 5. However, in case of series 5 + 6 + 7 is same as 7 + 6 + 5.

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