Five positive integers A, B, C, D and E
, with A < B < C < D < E
, are such that:
(i) A, B and C
(in this order) are in arithmetic sequence, and:
(ii) B, C and D
(in his order) are in geometric sequence, and:
(iii) C, D and E
(in this order) are in harmonic sequence
Determine the minimum value
such that there are precisely two quintuplets (A, B, C, D, E)
that satisfy all the given conditions.
: Try to solve this problem analytically, although computer program/ spreadsheet solutions are welcome.
One sequence (no proof of minimum value) that follows the requirements given by (i), (ii) and (iii) is: (2, 4, 6, 9, 18).
(i) The common difference between A, B and C is +2.
(ii) The common ratio between B, C and D is +3/2.
(iii) the common difference between the reciprocals of C, D and E is -1/18.
Edited on October 28, 2008, 10:43 am
Posted by Dej Mar
on 2008-10-28 10:38:15