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数列知识在高中(五年制基础段)数学课程中占有比较重要地位。很多年轻老师在讲授这部分知识时,总认为自己对此非常熟悉,掌握了很多好的解题方法,因此在教学前对教材只求表面理解,不作深入研究,教学没有新意,导致学生学习兴致不高。在具体教学过程中,有经验的老师往往会多加注意,正确引导学生进行有效学习。我们把数列看成是一种特殊的函数。数列的通项公式和前n项和的公式都可以看成是关于正整数n的函数,进而能够利用一次函数图像或二次函数图像,把许多数列问题转化为函数和方程,用数形结合的思想研究函数或数列,就是借助函数的图象进行直观分析,从而更有效地解决等差数列问题。
The knowledge of sequence occupies a more important position in mathematics curriculum of high school (five-year basic segment). Many young teachers always consider themselves very familiar with this part of the knowledge and have mastered a lot of good problem solving methods. Therefore, they need to understand the teaching materials only before the teaching, do not make further research, and have no new teaching, which leads students to learn more not tall. In the specific teaching process, experienced teachers tend to pay more attention to correctly guide students to learn effectively. We see the sequence as a special kind of function. The general formula of the series and the formulas of the first n terms and the sum of the series can be regarded as a function of a positive integer n so that many sequence problems can be transformed into functions and equations by using a one-time function image or a quadratic function image, The thought research function or series, is through the visual analysis of the function of the image, so as to more effectively solve the problem of arithmetic sequence.