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我们知道,教材就等差数列前n项和给出了两个公式:设等差数列{a_n}的前n项和公式和为S_n,公差为d,n∈N*,则S_n=na_1+n(n-1)/2d(公式一)S_n=(a_1+a_n)/2n(公式二)这两个公式在解决问题时如何使用,下面举例说明。以下m,n,p,q∈N*,不再说明。一、公式一的应用1.利用方程思想所谓方程思想就是将题目条件运用前n项和公式,表示成关于首项a1和公差d的两个方程,通过解决方程来解决问题。
We know that the textbook equals the first n terms of the difference and gives two formulas: Let the first n terms of the arithmetic progression {a_n} and the formula be S_n, the tolerance is d, n∈N *, then S_n = na_1 + n (n-1) / 2d (formula 1) S_n = (a_1 + a_n) / 2n (formula 2) How to use these two formulas to solve the problem, as an example. The following m, n, p, q∈N *, no longer specified. First, the application of a formula 1. The use of equation thinking The so-called equation of thought is the subject of conditions using the first n terms and formulas, expressed as the first a1 and tolerance d of the two equations, solve the problem by solving the equation.