# How To Calculate Harmonic Progression?

Short tutorial on how to calculate harmonic progression from arithmetic progression with formula and example.

## Harmonic Progression Series and Formula

Harmonic Progression in mathematical geometry is a sequence of real
numbers formed by taking the reciprocals of an arithmetic progression.

**Example**: The sequence 1,2,3,4,5 is an arithmetic progression, so its reciprocals 1/1,1/2,1/3,1/4,1/5 are harmonic progression.

**Harmonic Progression Series and Formula:**

**Harmonic Progression (H.P) = 1/a , 1/a+d, 1/a+2d, 1/a+3d.........1/a+kd**

**Where**,

a is the starting number in the sequence

d is the common difference between the numbers given in the sequence.

Let us learn here how to calculate harmonic progression from arithmetic progression with a neat example.

**Example:** Consider the sequence of arithmetic progression 3,5,7,9,11. Calculate harmonic progression.

**Given:**

A.P = 3,5,7,9,11

Starting Sequence = 3

Common Difference = 2

**Solution:**

Applying the values in the formula,

Harmonic Progression (H.P) = 1/3 , 1/3+2, 1/3+2(2), 1/3+3(2), 1/3+4(2)

Harmonic Progression (H.P) = 1/3 , 1/5, 1/7, 1/9, 1/11

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