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由递推公式求数列通项是高考考查数列通项的一种基本题型.由递推公式求通项通常是采用构造法或迭代法求通项.本文把常见的连续两项的递推公式的类型归纳如下.一、an-an-1=f(n)型例1在数列{an}中,已知a1=1,an=an-1+2n(n≥2),求an.解:an-an-1=n;an-1-an-2=2(n-1);…a2-a1=2×2.将以上各式左右分别相加得an-a1=n2+n-2.∴an=n2+n-1.一般地an-an-1=f(n)型递推公式,可通过累加求通项.
By recursion formula to calculate the number of items is a general examination of college entrance examination sequence of a basic questions by the recurrence formula to find the general term is to use the construction method or iterative method for the general term.This article recursive common two recurrence First, an-an-1 = f (n) Example 1 In the sequence {an}, we know that a1 = 1 and an = an- 1 + 2n (n≥2) Solution: a2 = a2 = 2 (n-1); a2 - a1 = 2 × 2. -2.∴an = n2 + n-1. In general, the an-an-1 = f (n) recursion formula can be obtained by adding up the terms.