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 \(n\ge1,\) the terms \(a_{2n-1}, a_{2n}, a_{2n+1}\) are in geometric progression, and the terms \(a_{2n}, a_{2n+1},\) and \(a_{2n+2}\) are in arithmetic progression. Let \(a_n\) be the greatest term in this sequence that is less than 1000. Find \(n+a_n.\)
(第二十二届AIME2 2004 第9题)