Mathematical Algorithms – Sequence & Series

Last Updated : 22 May, 2024

Mathematical algorithms are step-by-step procedures used to solve math problems. This article looks at sequences and series, which are important parts of these algorithms. Sequences are ordered sets of numbers, while series are the sums of these numbers. Understanding sequences and series is vital for solving complex math problems, modeling real-world situations, and developing advanced computer techniques. This article will give you a clear overview of the key ideas, uses, with some practice problems of mathematical algorithms involving sequences and series..

What is Sequence?

A sequence is an arrangement of a set of numbers in a particular order defined by some rule. If a ₁ , a ₂ , a ₃ . . . 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 a ₁ , a ₂ , a ₃ . . . is a sequence then the series is given as a ₁ + a ₂ + a ₃ + . . . 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 + . . .

Easy Problems on Sequence and Series:

Medium Problems on Sequence and Series:

Hard Problems on Sequence and Series:

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