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2 geometric progressions (III Soros Olympiad 1996-97 R1 10.3)

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May 29, 2024
algebrageometric progression

Problem Statement

An infinite sequence of numbers a,b,c,d,...a, b, c, d,... is obtained by term-by-term addition of two geometric progressions. Can this sequence begin with the following numbers:. a) 1,1,3,51,1,3,5 ? b) 1,2,3,51,2,3,5 ? c) 1,2,3,41,2,3, 4 ?
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