Question

The first and second term of a progression are "a" and "b" respectively. What is the third term if the progression is harmonic?

Answer 1

in a harmonic progression, the reciprocals of its terms form an arithmetic progression.

so if the third term of the HP is x

then 1/a , 1/b, and 1/x form an AP
that is,
1/b - 1/a = 1/x - 1/b
2/b - 1/a = 1/x
(2a - b)/(ab) = 1/x
x = ab/(2a - b)