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A sequence of positive integers with a_1 = 1 and a_9 + a_{10} = 646 is formed so that the first three terms are in geometric progression, the second, third, and fourth terms are in arithmetic progression, and, in general, for all \(n\geq1\), the terms, a_{2n-1}, a_{2n}, a_{2n + 1} are in geometric progression, and the terms, a_{2n}, a_{2n + 1}, and a_{2n + 2} , and  are in arithmetic progression. Let a_n be the greatest term in this sequence that is less than 1000. Find a_n.

Mar 20, 2018
edited by Guest  Mar 20, 2018

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I am a little confused on the notations, can you please use latex? Then I can attempt the problem

Mar 20, 2018
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Just underscores

Guest Mar 20, 2018
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A sequence of positive integers with a_1 = 1 and a_9 + a_{10} = 646 is formed so that the first three terms are in geometric progression, the second, third, and fourth terms are in arithmetic progression, and, in general, for all \(n\geq1\) , the terms, a_{2n-1}, a_{2n}, a_{2n + 1} are in geometric progression, and the terms, a_{2n}, a_{2n + 1}, and a_{2n + 2} , and  are in arithmetic progression. Let a_n be the greatest term in this sequence that is less than 1000. Find a_n.

Mar 21, 2018
edited by heureka  Mar 21, 2018