LEARN TESTS

Harmonic Progressions - Fundamentals

03 min read

The sequence a1, a2, …. an (where ai ≠ 0 for each i) is said to be in harmonic progression if the sequence 1/a1, 1/a2, … 1/an is in A.P.
The nth term of the H.P is given by an = 1 / a + (n - 1)d where a = 1 / aand d = 1/a2 - 1/a1
If a and b are 2 non - zero numbers then the harmonic mean of a and b is a number H
such that the sequence a , H, b is a H.P. We have, H = 2ab / (a + b)

If a1, a2, … an are n non - zero numbers then the harmonic mean H is given by
1/H= 1/N(1/a1 + 1/a2 +… 1/an)


POST A NEW COMMENT