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Bundeswettbewerb Mathematik 1994 Problem 1.4

Source: Bundeswettbewerb Mathematik 1994 Round 1

October 12, 2022
arithmetic sequencegeometric sequencerationalalgebra

Problem Statement

Let a,ba,b be real numbers (b≠0b\ne 0) and consider the infinite arithmetic sequence a,a+b,a+2b,….a, a+b ,a +2b , \ldots. Show that this sequence contains an infinite geometric subsequence if and only if ab\frac{a}{b} is rational.
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