By Team Aakash Byju's
Learn About Types of Sequence and Series in Maths
Sequences can be of two types, i.e. infinite sequence and finite sequence.
Finite series: 1,4,7,10 Infinite series.:4,6,8,....
Example:
Types of Sequence and Series:
1. Arithmetic Sequences and Series 2. Geometric Sequences and Series 3. Harmonic Sequences and Series
Arithmetic Sequences:
An arithmetic sequence is one in which each term is either the addition or subtraction of a common term known as the common difference.
1. 1, 3, 5, 7, ...
Example:
Arithmetic Series:
The arithmetic series is a series formed by using an arithmetic sequence.
Example:
1. 1+3+5+7, ...
Geometric Sequences:
A geometric sequence is one in which all of the terms have the same ratio.
Example:
1. 1, 4, 16, 64,....
Geometric Series:
The geometric series is a series formed using geometric sequence.
Example:
1+4+16+64,....
Harmonic Sequences:
A harmonic sequence is one in which each term of an arithmetic sequence is multiplied by the reciprocal of that term.
Example:
Harmonic Series:
The harmonic series is a series formed by using harmonic sequence.
Example:
Sequence and Series Formulas:
Arithmetic sequence
Arithmetic Series
Where, a=First term and d=Common difference.
Geometric Sequence and Series Formula
Geometric sequence
Geometric Series
Where, a=First term and r=Common ratio.