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.

amandapaolars Mar 20, 2018

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Mar 20, 2018

#1**0 **

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

supermanaccz Mar 20, 2018

#3**0 **

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.

see link: https://web2.0calc.com/questions/a-sequence_11

heureka Mar 21, 2018