大家知道,公差是d的数列{a_n}的通项为:a_n=a_1+(n-1)d,即a_n=dn+(a_1-d),可以把它看做n的一次函数,其图像是以d为斜率,纵轴截距为a_1-d的一条直线。当n∈N时,在直线上的对应点为(1,a_1),(2,a_2)…,(n,a_n)的点集,是该直线点集的一个子集。我们可以利用这种关系,巧解有关等差数列问题。例1 已知等差数列{a_n}的项a_m=n,a_n=m(m≠ As we all know, the general term for the series {a_n} of tolerance d is: a_n=a_1+(n-1)d, that is, a_n=dn+(a_1-d), it can be seen as a linear function of n. Its image is d is the slope, and the intercept on the vertical axis is a_1-d. When n∈N, the corresponding points on the straight line are (1, a_1), (2, a_2)..., (n, a_n) the point set, which is a subset of the straight point set. We can use this relationship to understand the problem of arithmetic series. Example 1 Known items a_m=n, a_n=m(m≠m) of the arithmetic progression sequence {a_n}