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Harmonic Progression is considered one of the most asked concept.
9 Questions around this concept.
If are in H.P., then the expression
is equal to:
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.
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Mathematics Textbook for Class VII
Page No. : 5.18
Line : 32
July 04, 2019
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