1959 AHSME Problems/Problem 33
Problem
A harmonic progression is a sequence of numbers such that their reciprocals are in arithmetic progression.
Let represent the sum of the first
terms of the harmonic progression; for example
represents the sum of
the first three terms. If the first three terms of a harmonic progression are
, then:
Solution
Given HP =
\\
So,
,
,
are in
. \\
Then, common difference
\\
Finding the fourth term of this
by
is trivial. \\
So, fourth term of Harmonic Progression
\\
Now,