探求数列通项公式是学生很感兴趣的课题。高中《代数》(甲种本)第二册教学参考书第40页有这样一段话,“某学生在5次数学测验中的成绩组成的数列:89,95,78,90,82就写不出它的通项公式。”果真如此吗?我把这个问题交给学生思考。我首先讲了一点预备知识:①数列的实质是函数,已知数列的前面 N 项相当于已知了 N 点坐标:(1,a_1),(2,a_2),……(N,a_n)。②过不在一直线上的三点,可以确定一条抛物线 y=ax~2+bx+c。由此学生产生联想:不共线的 N 个点,可以确 Exploring the sequence formula is a topic of great interest to students. High School “Algebra” (A book) Volume II Teaching Reference Page 40 has such a passage, “a student in five math test scores composed of the series: 89,95,78,90,82 write Out of its general formula. ”If so? I give this question to students thinking. First of all, I have a little preparation knowledge: ① The essence of a sequence is a function. The first N terms of the known sequence correspond to the coordinates of N points known: (1, a_1), (2, a_2), ...... (N, a_n) . ② is not in a straight line at three o'clock, you can determine a parabola y = ax ~ 2 + bx + c. Thus the students produce Lenovo: N points are not collinear, can be true