Four positive integers P, Q, R and S with P < Q < R < S are such that P, Q and R (in this order) are in arithmetic sequence and Q, R and S (in this order) are in harmonic sequence.

Given that S - P = 19, determine all possible quadruplet(s) (P, Q, R, S) that satisfy the given conditions.

I only found one quadruplet that satisfies the given conditions:
(72, 78, 84, 91).

The constant value between the successive terms of the arithemetic sequence of 72, 78, and 84 is +6.

The constant value between the successive terms of the
arithmetic sequence 1/78, 1/84, 1/91 (i.e., harmonic sequence of 78, 84, 91) is -1/1092. 

Posted by Dej Mar on 2008-07-22 04:02:43