数列

• 作 者: 段志波
• 机 构: 湖北省江陵中学,
• 出 处: 语数外学习(高中版下旬)
• 发表日期: 2015年01期

在数列这一章中,除等差、等比数列之外,递推数列的应用是非常普遍,递推数列的形式是多种多样。在这里对一类数列作一个说明。形如:xa_(n+1)=ya_n+f(n)(x、y为常数)①x=y≠0 f(n)为常函数,则{a_n}为等差数列。②x≠y且xy≠0,f(n)为常数函数。例1:a_(n+1)=2a_n+3,a_1=1,求{a_n}通项。解:a_n+1+3=2{a_n+3}

In the sequence of numbers, the use of recursion sequences is very common except for the arithmetic and geometric ones, and the forms of recursion sequences are varied. Here a description of a series of numbers. For example: xa_ (n + 1) = ya_n + f (n) (x, y are constants) ①x = y ≠ 0 f (n) is a constant function, then {a_n} is an arithmetic sequence. ② x ≠ y and xy ≠ 0, f (n) is a constant function. Example 1: a_ (n + 1) = 2a_n + 3, a_1 = 1, seek the {a_n} general term. Solution: a_n + 1 + 3 = 2 {a_n + 3}