Difference Between Sequence and 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. 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.

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. General Form: \([p_{i}]_{i=1}^{n}\). Unending sequence like p1, p2, p3, p4, p5, p6, . . . . , pn, . . . . . , is known as an infinite sequence. General Form: \([p_{n}]_{n=1}^{\infty }\).

Series can also be classified as a finite and infinite series. A finite series can be represented as m1 + m2 + m3 + m4 + m5 + m6 + . . . . . + mn and an Infinite series can be written as m1 + m2 + m3 + m4 + m5 + m6 + . . . . . + mn + . . . . . If m1 + m2 + m3 + m4 + m5 + m6 + . . . . . . + mn = Sn, then Sn is termed as the sum to n elements of the series. 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.

Practise This Question

There were two sacks containing numbers, sack A contained the set of positive integers while sack B contained the set of whole numbers. Which sack contains more numbers?

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