All about flooble | fun stuff | Get a free chatterbox | Free JavaScript | Avatars    
perplexus dot info

Home > Numbers > Sequences
Three Sequences (Posted on 2004-01-06) Difficulty: 3 of 5
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)

See The Solution Submitted by Brian Smith    
Rating: 3.0000 (2 votes)

Comments: ( Back to comment list | You must be logged in to post comments.)
Answer | Comment 8 of 9 |

There are precisely three possible sets (S) of six positive whole
numbers which satisfy conditions of the problem and these are:

(I) S = {3, 4, 5, 6, 12, 24} ; arirhmetic sequence (A) = {3, 6, 12, 24}; geometric sequence (G) = {3, 6, 12, 24}; harmonic sequence(H) = {3, 4, 6, 12}

(II) S = {3, 4, 6, 9, 12, 24} ; A = {3, 6, 9, 12};
G = {3, 6, 12, 24}; H= {3, 4, 6, 12)

(III) S = {3, 4, 6, 12, 18, 24} ; A = {6, 12, 18, 24};
G = {3, 6, 12, 24}; H= {3, 4, 6, 12);

Edited on March 18, 2008, 11:11 am
  Posted by K Sengupta on 2007-05-25 11:30:56

Please log in:
Login:
Password:
Remember me:
Sign up! | Forgot password


Search:
Search body:
Forums (0)
Newest Problems
Random Problem
FAQ | About This Site
Site Statistics
New Comments (4)
Unsolved Problems
Top Rated Problems
This month's top
Most Commented On

Chatterbox:
Copyright © 2002 - 2017 by Animus Pactum Consulting. All rights reserved. Privacy Information