一、形如an+1=pan+q(p、q为常数)的一阶线性式其特征方程为x=px+q,特征根为α.方法一:通过待定系数法,转化成an+1+m=p(an+m),如an+1=3an+6,设an+1+m=3(an+m),利用两式等价得m=3,即原式可转化为an+1+3=3(an+3),即数列an+3是以3为公比的等比数列.方法二:两边同时减去特征根α,也可将已知转化成an+1+m=p(an+m).如an+1=-2an+6,特征方程为x=-2x+6,x=2,同时 1. First-order linear equations of the form an+1 = pan + q (p, q are constants) whose characteristic equation is x = px + q, and the eigenvalue is α. Method 1: Through undetermined coefficient method, it is converted into an + 1+m=p(an+m), if an+1=3an+6, set an+1+m=3(an+m), use two equations to get m=3, that is, the original formula can be converted into An+1+3=3(an+3), that is, the series an+3 is a geometric array with 3 as the common ratio. Method 2: the eigenvalue α is subtracted on both sides simultaneously, and the known is also converted into an+1. +m=p(an+m). If an+1=-2an+6, the characteristic equation is x=-2x+6, x=2, and