perplexus.info :: Sequences : Three Sequences

Three Sequences (Posted on 2004-01-06)

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)

Submitted by Brian Smith

Rating: 3.0000 (2 votes)

Solution: (Hide)

There are three similar sets which satisfy the constraints of the problem:
Set Arithmetic Geometric Harmonic 3,4,5, 6,12,24 3, 4, 5, 6 3,6,12,24 3,4,6,12 3,4,6, 9,12,24 3, 6, 9,12 3,6,12,24 3,4,6,12 3,4,6,12,18,24 6,12,18,24 3,6,12,24 3,4,6,12

They use the same harmonic and geometric sequences.
SilverKnight outlines a method to find them here.

Comments: ( You must be logged in to post comments.)

Subject	Author	Date
Puzzle Solution With Explanation	K Sengupta	2007-05-25 11:32:51
Answer	K Sengupta	2007-05-25 11:30:56
re: question	Charlie	2004-01-07 09:13:53
question	Victor Zapana	2004-01-06 21:51:02
re(2): Solution	Gamer	2004-01-06 16:07:56
re: Solution	stan	2004-01-06 15:15:01
Solution	stan	2004-01-06 14:55:14
re: solution	SilverKnight	2004-01-06 14:09:13
solution	SilverKnight	2004-01-06 13:57:02

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