一道数列习题的解法反思与演变

• 作 者: 张继海
• 出 处: 试题与研究
• 发表日期: 2012年29期
• 关键词: 变式 道数 分类讨论思想 化归思想 通项公式 隐含条件 解题思路 调和数列 不小于 结论项

一、试题及解题目:已知Sn是等比数列{an}的前n项和,S3,S9,S6成等差数列,求证:a2,a8,a5成等差数列.(人教A版必修⑤P61习题2.5第6题)分析:本题文段简练、字符清爽(两个已知事项,一个结论项).“等比”两字要特别关注,没有说公比是否为1(但知道q≠0,于是应讨论).其次应抓住:等差数列,且三个字母的顺序不能乱(包括对结论的理解亦如此).

First, the test questions and problem solving: Sn is known to be the first n items of the geometric sequence {an} and, S3, S9, S6 into arithmetic sequence, verify: a2, a8, a5 into arithmetic sequence. Version of the compulsory ⑤ P61 Exercise 2.5 sixth question) Analysis: The title section concise, fresh characters (two known issues, a conclusion). “Equal ” should pay special attention to the word, did not say whether the public is 1 ( But we know that q ≠ 0, so we should discuss it.) Second, we should grasp: the arithmetic sequence, and the order of the three letters can not be chaos (including the understanding of the conclusion is also true).