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In mathematics, a harmonic progression (or harmonic sequence) is a progression formed by taking the reciprocals of an arithmetic progression. Equivalently, a sequence is a harmonic progression when each term is the harmonic mean of the neighboring terms.
- What is harmonic sequence formula?
- Why is it called harmonic sequence?
- What is the nth term in the harmonic sequence?
What is harmonic sequence formula?
A Harmonic Progression (HP) is defined as a sequence of real numbers which is determined by taking the reciprocals of the arithmetic progression that does not contain 0. ... The formula to calculate the harmonic mean is given by: Harmonic Mean = n /[(1/a) + (1/b)+ (1/c)+(1/d)+….]
Why is it called harmonic sequence?
Its name derives from the concept of overtones, or harmonics in music: the wavelengths of the overtones of a vibrating string are 12, 13, 14, etc., of the string's fundamental wavelength.
What is the nth term in the harmonic sequence?
In order to solve a problem on Harmonic Progression, one should make the corresponding AP series and then solve the problem. As the nth term of an A.P is given by an = a + (n-1)d, So the nth term of an H.P is given by 1/ [a + (n -1) d].
