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Number theory Difficulty 3.0 AMC 10/12 Prove it Canada

Three positive integers $a$ , $ar$ and $ar^2$ form an increasing sequence. If the product of the three integers in this sequence is $216$ , determine all sequences satisfying the given conditions.

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Source: CEMC, University of Waterloo, licensed CC-BY-NC-4.0. Statement reproduced verbatim; metadata (topic, difficulty) added by this project. Solutions are the publisher's, linked not copied.