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)
Don't have a proof of it... but,
{3, 4, 6, 9, 12, 24} seems to work.
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Arithmetic:
3, 6, 9, 12
Geometric:
3, 6, 12, 24
Harmonic:
3, 4, 6, 12
(1/12, 1/6, 1/4, 1/3 make an arithmetic sequence)
solution
