# Sequences

## Geometric sequences

A sequence in which every term is obtained by multiplying or dividing a particular number with the preceding number is a geometric sequence. For example, the geometric progression, $$5, 10, 15, 20, 25, \cdots$$, has a common ratio of $$5$$.

## Harmonic sequences

A series of numbers is in harmonic sequence if the reciprocals of all the sequence elements form an arithmetic sequence, which does not contain $$0$$. In a harmonic sequence, any terms in the sequence are considered the harmonic means of its two neighbours.