例题给定常数c>0,定义函数f(x)=2|x+c+4|-|x+c|,数列a1,a2,a3,…满足an+1=f(an),n∈N*.(1)若a1=-c-2,求a2及a3;(2)求证:对任意n∈N*,有an+1-an≥c,;(3)是否存在a1,使得a1,a2,…an,…成等差数列?若存在,求出所有的a1;若不存在,说明理由.这是2013年高考上海理科卷的最后一题,也就是人们常说的压卷题或压轴题.下 Example Given the constant c> 0, the function f (x) = 2 | x + c + 4 | - | x + c | is satisfied and the sequence a1, a2, a3, ... satisfies an + 1 = f N *. (1) If a1 = -c-2, find a2 and a3; (2) Prove that for any n∈N *, there is an + 1-an≥c; , a2, ... an, ... into the arithmetic sequence? If present, find out all a1; if not, explain the reasons .This is the 2013 college entrance examination in Shanghai Science Volume last question, that is, people often say that the pressure roll Or finale questions