由一阶线性递推数列求数列的通项公式,在很多文章中都进行了研究,而且也得出了在不同情况下求通项公式很多方法,比如累加法,累乘法,构造法等.但是却很少有文章对所求通项公式结构进行探讨,关注问题的结构有利于清楚地研究问题.一、方法探究定理:若数列{an}满足a1=a,an+1=f(n)an+g(n),则an=(∏(n-1)(i=1)f(i))·a+∑(n-2)(j=1)(∏(n-1)(i>j)f(i))g(j)+g(n-1) The formulas of the general formulas for calculating the number of columns from the first-order linear recursion series have been studied in many articles, and many methods such as accumulation method, cumulative multiplication method, construction method and the like are also obtained in different situations. However, there are few articles that discuss the structure of the general formula, and focus on the structure of the problem is conducive to a clear study of the problem.First, the method to explore the theorem: if the sequence {an} satisfies a1 = a, an + 1 = f (n ) an + g (n), an = (Π (n-1) (i = 1) f (i)) · a + Σ (n-2) (j = 1) > j) f (i)) g (j) + g (n-1)