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.