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These problems deal with sequences of numbers. Can you spot what the sequences' rules are?
Each of A, B, C and D is a positive integer with A < B < C < D
having gcd(A, B, C, D) = 1 such that:

(i) A, B and C are in geometric sequence, and:
(ii) B, C and D are in arithmetic sequence, and:
(iii) A, B and D are in harmonic sequence.

Does there exist an infinite number of quadruplets satisfying the given conditions? Give reasons for your answer.

(No Solution Yet, 3 Comments) Submitted on 2014-10-19 by K Sengupta   
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