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What is harmonic progression? How can be identify a progression is in harmonic?
What is harmonic progression? How can be identify a progression is in harmonic?
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A sequence of real numbers that can be formed by taking the reciprocals of the arithmetic progression is called Harmonic progression. It does not contain 0. It is denoted by HP.
Any term of the harmonic progression is considered as the harmonic means of its two neighbors. For example, Let the sequence a, b, c, d, …is considered as an arithmetic progression; therefore the harmonic progression can be written as 1/a, 1/b, 1/c, 1/d, …
Harmonic Mean: Harmonic mean is the reciprocal of the arithmetic mean of the reciprocals. The formula is given by:
Harmonic Mean = n /[(1/a) + (1/b)+ (1/c)+(1/d)+….]
Where,
a, b, c, d are the values and n is the number of values present.
The nth term of the Harmonic Progression is given by:
H.P = 1/ [a+(n-1)d]
Where
a= first term of A.P
d=common difference
n=number of terms in A.P
We can identify whether a progression is in harmonic progression or not by checking the harmonic mean of the given progression.
