Harmonic Progression - Practice Questions & MCQ

Harmonic Progression

A sequence of non-zero numbers is called a harmonic progression if the sequence is an arithmetic progression.

OR

Reciprocals of arithmetic progression is a Harmonic progression.

Eg,  is an HP because their reciprocals 2, 5, 8, 11,... form an A.P.

• No term of the H.P. can be zero.

• The general form of HP is

            Here a is the first term and d is the common difference of corresponding A.P.

General term of a Harmonic Progression

The nth term or general term of a H.P. is the reciprocal of the nth term of the corresponding A.P.

Thus, if is an H.P. and the common difference of corresponding A.P. is d, i.e. , then the nth term of corresponding AP is  and hence, the general term or nth term of an H.P. is given by 

Note:

There is no general formula for the sum of n terms that are in H.P.