There are various types of sequences and series, in this section, we will discuss some special and most commonly used sequences and series. The types of sequence and series are:
- Arithmetic Sequences and Series
- Geometric Sequences and Series
- Harmonic Sequences and Series
Arithmetic Sequence and SeriesAn arithmetic sequence is a sequence where the successive terms are either the addition or subtraction of the common term known as common difference. For example, 1, 4, 7, 10, …is an arithmetic sequence. A series formed by using an arithmetic sequence is known as the arithmetic series for example 1 + 4 + 7 + 10… is an arithmetic series.
Geometric Sequence and SeriesA geometric sequence is a sequence where the successive terms have a common ratio. For example, 1, 4, 16, 64, …is an arithmetic sequence. A series formed by using geometric sequence is known as the geometric series for example 1 + 4 + 16 + 64… is a geometric series. The geometric progression can be of two types: Finite geometric progression and infinite geometric series.
Harmonic Sequence and SeriesA harmonic sequence is a sequence where the sequence is formed by taking the reciprocal of each term of an arithmetic sequence. For example, 1, 1/4, 1/7, 1/10,… is a harmonic sequence. A series formed by using harmonic sequence is known as the harmonic series for example 1 + 1/4 + 1/7 + 1/10…. is a harmonic series.