一阶线性差分方程xn+1=kxn+b是个十分有用的数学模型,本文就其性质做了初步探讨和推广并说明了其在解题中的应用·性质1方程xn+1=kxn+b中,当b=0(即方程为齐次方程)时,其解为等比数列;当k=1(即差分方程为常数)时其解为等差数列·性质2方程xn+1=kxn+b(k≠0),若满足x1=m,则其解为x The first-order linear difference equation xn+1=kxn+b is a very useful mathematical model. This article makes a preliminary discussion of its properties and generalizes and illustrates its application in solving problems. Properties 1 Equation xn+1=kxn+b When b=0 (that is, the equation is a homogeneous equation), the solution is an equal-ratio series; when k=1 (that is, the difference equation is a constant), the solution is an arithmetic sequence. The property 2 equation xn+1=kxn +b(k≠0), if x1=m is satisfied, the solution is x