2013年上海高考理科数学压轴题如下:给定常数c>O,定义函数f(x)=2|x+c+4|-|x+c|.数列a1,a2,a3,…满足a_(n+1)=f(a_n),n∈N*.(1)若a1=-c-2,求a2及a3;(2)求证:对任意n∈N*,a_(n+1)-a_n≥c;(3)是否存在a1,使得a1,a2,a3,…,an,…成等差数列?若存在,求出所有这样的a1;若不存在,说明理由.一、试题评析本题具有如下特点:(1)这是一道涉及函数、数列与不等式的综合题,函数、数列与不等式都是高中数学课程中的核心内容,因此本题较好地体现了“重点内容重点考查”这一命题指导思想,同时本题也体现了“在知识点交汇处命题”这一命题原 2013 Shanghai college entrance examination science finale questions as follows: given constant c> O, define the function f (x) = 2 | x + c + 4 | - | x + c | (1) If a1 = -c-2, find a2 and a3; (2) Verify that for any n∈N *, a_ (n + 1) - a_n≥c; (3) Is there any a1 such that a1, a2, a3, ..., an, ... become equal-difference sequences? If yes, then find all such a1; if not, explain the reasons. It has the following characteristics: (1) This is a comprehensive question involving functions, numbers and inequalities. Functions, numbers and inequalities are all the core contents of high school mathematics curriculum. Therefore, this question better reflects the key points of “ This proposition guiding ideology, at the same time this question also embodies the proposition ”at the intersection of knowledge points" proposition