Question

Derive the formula for the general term of an HP

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Answer 1

A Harmonic Progression is such type of progression in which the reciprocal of terms forms as Arithmetic Progression.

So, if we consider an AP with first term as 'a' , common difference as 'd' and number of terms as 'n' .

Progression would be :

$\mathsf { a , \: a \: + \: d , \: a \: + \: 2d, \: a \: + \: 3d , \: ....... \: , \: a \: + \: ( \: n \: - \: 1 \: )d }$

As per the definition, the reciprocals of each term will form Harmonic Progression.

Hence, our HP is :

$\mathsf{ \dfrac{1}{a} ,\: \dfrac{1}{a \: + \: d} ,\: \dfrac{1}{a \: + \: 2d} ,\: \dfrac{1}{a \: + \: 3d} ,\: ..... \: ,\dfrac{1}{a \: + \: (n \: - \: 1)d} }$

Hence, the general term of the HP will be :

$\mathsf{ = \: \dfrac{1}{a \: + \: (n \: - \: 1)d} }$

Answer 2

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