8.
有一個數列，\( a_1=1 \)且\( a_9+a_{10}=646 \)。此數列的第一、第二、第三項成等比數列，第二、第三、第四項成等差數列；且一般而言，對所有的\( n \ge 1 \)，\( a_{2n-1},a_{2n} \)及\( a_{2n+1} \)成等比數列，\( a_{2n},a_{2n+1} \)及\( a_{2n+2} \)成等差數列。設\( a_k \)為此數列中小於1000的最大項，試求\( k= \)？
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 \( n \ge 1 \), 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 \( n+a_{n} \).
(2004AIME第九題，
http://www.artofproblemsolving.c ... id=45&year=2004)
點題號會跳到討論文章
中文題目應該是從這裡抄出來的，檔案就少了正整數這個條件
h ttp://e-tpd.kssh.khc.edu.tw/sys/read_attach.php?id=866 連結已失效
