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近些年来,数列与函数的综合是高考考查学生数学能力的重点与热点,同时也是难点.因为利用函数思想解决数列问题时,不但需要学生掌握数列知识,还需要学生具备充分利用函数知识的能力.本文例谈函数思想在数列中的应用.1.函数的定义在数列中的应用例1给出以下三个结论:1{an}是等差数列的充要条件是an是n的一次函数;2{an}是等差数列的充要条件是其前n项和Sn是n的二次函数;
In recent years, the combination of numbers and functions is the focus and hot spot for examining students’ math ability in college entrance examination, which is also difficult at the same time.When using function thinking to solve sequence problems, students not only need to acquire sequence knowledge, but also need students to have the ability to make full use of function knowledge . This article gives an example of the application of the functional idea in a sequence. 1. The application of the definition of a function in a sequence Example 1 gives the following three conclusions: 1 {an} is a necessary and sufficient condition for an algebraic sequence is an is a linear function of n ; 2 {an} is an algebraic sequence if its first n terms and n is a quadratic function of n;