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数列的通项公式是数列的基础知识,根据数列的递推公式求其通项公式,常见求法有累加法、累乘法、a_n与S_n的关系,以及构造法.对于“已知数列{a_n}满足:a_1=a,a_2=b,且pa_n+qa_(n+2)=ha_(n+1),求该数列的通项公式”这类问题,在数学竞赛中出现的较多,它的难度取决于系数p,q,h的取值情况,现笔者就这类问题利用构造等比数列对各种情况进行分析来探求求该数列通项的一个通法.1.实例分析
The general formula of a sequence of numbers is the basic knowledge of the sequence, and its general formulae are calculated according to the recursive formulas of the series. The common methods of summation include the accumulation method, the cumulative multiplication method, the relationship between a_n and S_n, and the construction method. For the known series {a_n } Satisfaction: a_1=a, a_2=b, and pa_n+qa_(n+2)=ha_(n+1), find a general term formula for this series. Its difficulty depends on the value of the coefficients p, q, h. Now the author uses the structural analogy series to analyze various situations to find a common method for finding the general term of the series.