Harmonic Progression

Harmonic Progression

## Definition / Concept

A sequence is in harmonic progression if the reciprocals of its non-zero terms form an AP.

## Formula

If:

$$a_1,a_2,a_3,\ldots$$

are in HP, then:

$$\frac1{a_1},\frac1{a_2},\frac1{a_3},\ldots$$

are in AP.

The general term can be written as:

$$\frac1{a_n}=A+(n-1)d$$

Therefore:

$$a_n=\frac1{A+(n-1)d}$$

## Usage

- Used to identify HPs and convert HP problems into AP problems.