**Harmonic Progression**and denoted as

**H.P**Here will teach you about Geometric Sequences and Series.

H.P = *1*a, *1*a + d, *1*a+2d, *1*a+(n-1)d, ….,*1*a+(n-1)d,….

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

H.P = *1*A.P

**Theorem**: A sequence is a harmonic progression if and only if its terms are the reciprocals of an arithmetic progression that doesn’t contain 0.0.

**Harmonic Mean**

The harmonic mean can be expressed as the reciprocal of the arithmetic mean of the reciprocals of the given set of observations.

If H(a,b) is the harmonic mean, A(a,b) is arithmetic mean and G(a,b) is geometric mean of real no. a and b.

A(a,b) = *a + b*2

G(a,b) = √ab

H(a,b) = *1*A(1/a,1/b)

H(a,b) = *1**a+b*2ab

H(a,b) = *2ab*a + b

**Relationship between H.P, A.P and G.P**

H(a,b) = *2ab*a + b = *ab**a+b*2

H(a,b) = *G(a,b) ^{2}*A(a,b)

H(a,b).A(a,b) = G(a,b)^{2}

I hope, this article will help you a lot to understand the **Harmonic Sequence **. If you still have any doubts and problems with any topic of mathematics you can ask your problem in the Ask Question section. You will get a reply shortly.

Sequence and Series | Progression | Type of Sequence

Arithmetic Sequences and Series | Arithmetic Mean

Geometric Sequences and Series | Geometric Mean

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