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在等差数列{a_2}中,a_n=a_1+(n-1)d和S_n=na_1+1/2n(n-1)d即a_2=dn+(a_1-d)……(1)和S_n=1/2dn~2+(a_1-1/2d)n……(2)分别是特殊的一次函数和二次函数。(1)式的图象是直线y=dx+(a_1-d)上一系列的点(1,a_1),(2,a_2),…,(n,a_n),…,的集合,(2)式的图象是抛物线y=1/2dx~2+(a_1-1/2d)x上的一系列的点(1,S_1),(2,S_2),…,(n,S_n),…,的集合。根据上面的这种几何意义,对于等差数列,我们可以得到下面的一些关系。
In the equal difference sequence {a_2}, a_n=a_1+(n-1)d and S_n=na_1+1/2n(n-1)d, that is, a_2=dn+(a_1-d)...(1) and S_n=1 /2dn~2+(a_1-1/2d)n...(2) are special primary functions and quadratic functions, respectively. The image of equation (1) is a set of points (1,a_1), (2,a_2),...,(n,a_n),...,, for a series of lines y=dx+(a_1-d), (2) The image of the formula is a series of points (1, S_1), (2, S_2),..., (n, S_n),..., on the parabola y=1/2dx~2+(a_1-1/2d)x. Collection. Based on this geometrical meaning above, we can get the following relations for the arithmetic progression.