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Sum from Arithmetic and Geometric (Posted on 2016-03-24) Difficulty: 3 of 5
Each of A, B and C is a positive integer such that:
20*A, 6*B and C are in arithmetic sequence, and:
20*A, 6*B and C+1 are in geometric sequence

Find the six smallest values of A+B+C

No Solution Yet Submitted by K Sengupta    
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re: Possible Solution | Comment 2 of 5 |
(In reply to Possible Solution by Jer)

I found (A,B,C) = (5,15,80) is an answer with progressions 100, 90, 80 or 81.  This corresponds to d=-10.  The sum A+B+C is 120 in this case.

Similarly, d=-30 yields (A,B,C) = (45, 145, 840) for a sum of 1030 and d=-40 yields (A,B,C) = (80, 780, 1520) for a sum of 2380.

Also, you have a typo C=d(d+1) should be C=d(d+2)

  Posted by Brian Smith on 2016-03-24 13:52:42
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