A set of six positive integers contains an arithmetic sequence of four terms, a geometric sequence of four terms, and a harmonic sequence of four terms. What are the numbers in the set when the largest member of the set is a minimum?

Note: A harmonic sequence is a sequence whose reciprocals form an arithmetic sequence. ex: ({10, 12, 15, 20} is harmonic since {1/10, 1/12, 1/15, 1/20} is arithmetic)

(In reply to re: Solution by stan)

Actually that's a good place to start. Think if 1,2,3,4, then note 1,2,4, so add 1/2. Then note if you add 3/2 it's harmonic. THEN, multiply the whole sequence by 6. :)

Posted by Gamer on 2004-01-06 16:07:56