阅读贵刊2015年3月下刊登课外练习题,笔者通过不同途径,另解其中两道题.题一(初一(2)1)已知n个正整数按其规律排列如下a_1,a_2,a_3…a_n,且a_1=1,a_2=10,a_3=35,a_4=84,试求第n个整数a_n.解从其排列规律可以认为a_1=1=1~2,a_2=10=1~2+3~2,a_3=35=1~2+3~2+5~2,a_4=84=1~2+3~2+5~2+7~2,……则a_n=1~2+3~2+5~2…+(2_n-1~)2.由S=1~2+2~2+3~2+…+(2_n)~2 Read your article published in March 2015 under the extracurricular exercises, the author through different channels, another solution to two questions .Third (first (2) 1) n positive integers are arranged according to their rules as follows a_1, a_2, a_3 ... a_n, and a_1 = 1, a_2 = 10, a_3 = 35, a_4 = 84, try to find the nth integer a_n. From the arrangement rule, we can consider a_1 = 1 = 1 ~ 2 and a_2 = 10 = 2 + 3~2, a_3 = 35 = 1~2 + 3~2 + 5~2, a_4 = 84 = 1~2 + 3~2 + 5~2 + 7~2, ... then a_n = 1~2 + 3 ~ 2 + 5 ~ 2 ... + (2_n-1 ~) 2. From S = 1 ~ 2 + 2 ~ 2 + 3 ~ 2 + ... + (2_n)