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近年来,高考试题“根植课本,灵活变通,体现能力”的命题趋势日益稳定.因此树立“立足课本,变式提高,培养能力”的指导思想,引导学生挖掘教材内涵,充分利用例(习)题的潜在功能,优化学生思维品质,是提高复习质量的关键保证.本文就指导学生搞好数列复习的具体做法,谈几点体会.一、重视“主元”的统领作用数列{a_n}的通项 a_n 与其前 n 项和 S_n 组成了数列{a_n}的“主元”,包括等差(比)数列的所有问题,都是围绕这两个“主元”展开.它们之间具有关系:a_1=S_1,a_n=S_n-S_(n-1)(n≥2).例1 设{a_n}是正数组成的数列,其前 n 项和为S_n,并且对所有自然数 n,a_n 与2的等差中项等于 S_n 与2的等比中项,求数列{a_n}的通项公式.
In recent years, the propositional trend of “high school textbooks, flexibility, and ability to reflect” has become increasingly stable. Therefore, we have established the guiding ideology of “base on textbooks, and improve and cultivate abilities” to guide students in tapping the content of textbooks and make full use of examples. The potential functions of the questions and the optimization of student’s thinking quality are the key guarantees for improving the quality of review. This article guides students on how to do a series of review of specific practices and discusses several points of experience. First, pay attention to the “leadership” of the leading role of the series {a_n} The general term a_n and its predecessors and S_n constitute the “principal element” of the sequence {a_n}, including all the problems of the arithmetic difference sequence, all around these two “principal elements”. They have a relationship between them: A_1=S_1,a_n=S_n-S_(n-1)(n≥2). Example 1 Let {a_n} be a series of positive numbers whose first n terms are S_n, and for all natural numbers n, a_n and 2 The equal-difference term is equal to the equal-magnitude term of S_n and 2, and the general term of the series {a_n} is obtained.