Mathematical Algorithms | Sequence & Series

Last Updated : 26 Sep, 2023

What is Sequence?

A sequence is an arrangement of a set of numbers in a particular order defined by some rule. If a1, a2, a3 . . . is a sequence then 1, 2, 3 denotes the position of the elements in the sequence. A sequence can be finite or infinite.

Some well-known sequences are:

What is a Series?

A series is formed by adding the elements of the sequence. If a1, a2, a3 . . . is a sequence then the series is given as a1 + a2 + a3 + . . . Note that the series refers to the indicated sum of the sequence, not the sum itself.

Difference between Sequence and Series:

Sl. No. Sequence Series
1 It is a set of elements that follow a particular pattern. A Series is the sum of the elements of a sequence.
2 Order of the element is very important. Order of the elements is not so important.
3 Finite Sequence: 1, 2, 3, 4, 5
Infinite Sequence: 1, 2, 3, . . .
Finite Series: 1 + 2 + 3 + 4 + 5
Infinite Series: 1 + 2 + 3 + . . .

Some practice problems on Sequence and Series:

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