Sequence and Series Definition
A sequence is defined as a successive arrangement of numbers in an order according to some specific rules. Let x1, x2, x3, x4,… be the terms of a sequence, where 1, 2, 3, 4,… represents the term’s position in the given sequence.
- Depending upon the number of terms in a sequence, it is classified into two types, namely a finite sequence and an infinite sequence.
- A series is formed by adding the elements of a sequence.
If x1, x2, x3, x4, ……. is the given sequence, then its corresponding series is given by SN = x1+x2+x3 + .. + xN
- Depending on whether the sequence is finite or infinite, the series can be either finite or infinite.
Sequences and Series Formulas
Sequences and Series Formulas: In mathematics, sequence and series are the fundamental concepts of arithmetic. A sequence is also referred to as a progression, which is defined as a successive arrangement of numbers in an order according to some specific rules. A series is formed by adding the elements of a sequence.
Let us consider an example to understand the concept of a sequence and series better. 1, 3, 5, 7, 9 is a sequence with five terms, while its corresponding series is 1 + 3 + 5 + 7 + 9, whose value is 25.
This article explores the sequences and series formulas, including arithmetic, geometric, and harmonic series.
Table of Content
- Sequence and Series Definition
- Types of Sequences and Series
- Arithmetic Sequence and Series
- Geometric Sequence and Series
- Harmonic Sequence and Series
- Fibonacci Numbers
- Sequences and Series Formulas
- Difference Between Sequences and Series
- Sequences and Series Formulas Examples