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A.P and G.P

Source: 2018 Taiwan APMO preliminary

November 10, 2020
algebrageometric sequence

Problem Statement

Let (i) a1,a2,a3a_1,a_2,a_3 is an arithmetic progression and a1+a2+a3=18a_1+a_2+a_3=18 (ii) b1,b2,b3b_1,b_2,b_3 is a geometric progression and b1b2b3=64b_1b_2b_3=64 If a1+b1,a2+b2,a3+b3a_1+b_1,a_2+b_2,a_3+b_3 are all positive integers and it is a ageometric progression, then find the maximum value of a3a_3.
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