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 question by Victor Zapana)

Regarding "What is meant by "largest member of the set is a minimum"? Does it mean, which I think it does, that the largest number is the smallest as well? Well, if thats the case, then probably all the numbers in the set are the same? "

I'm sure it just means that the largest member of this set is smaller than the largest member of any other set that satisfies these properties.

Posted by Charlie on 2004-01-07 09:13:53