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HMMT Algebra/NT 2019/5: Next term of arithmetico-geometric sequence

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February 17, 2019
HMMTalgebra

Problem Statement

Let a1,a2,…a_1, a_2, \dots be an arithmetic sequence and b1,b2,…b_1, b_2, \dots be a geometric sequence. Suppose that a1b1=20a_1 b_1 = 20, a2b2=19a_2 b_2 = 19, and a3b3=14a_3 b_3 = 14. Find the greatest possible value of a4b4a_4 b_4.
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