20 0 2年《通讯杯》高中数学综合应用能力竞赛试题中的第 1 5题是这样的 :设数列 {ａｎ}是一个公差不为零的等差数列 ,ａ5 =6 .1 )当ａ3 =3时 ,请在数列 {ａｎ}中找一项ａｍ,ｍ 5,使得ａ3 ,ａ5 ,ａｍ 成等比数列 ;2 )当ａ3 =2时 ,若自然数ｎ1,ｎ2 ,… ,ｎｔ,… ,满足 5ｎ1ｎ The 1st question in the 2020 “Communication Cup” high school mathematics comprehensive application competency test question is this: Let the series {an} be an arithmetic progression with a non-zero tolerance, a5 =6.1) when a3 = At 3 o’clock, find an am, m 5 in the series {an} so that a3, a5, and am become equal numbers; 2) When a3 = 2, if the natural numbers n1, n2, ..., nt, ..., are satisfied 5n1n