数列问题 数列是高中数学的重要内容，又是学习高等数学的基础。高考对本章的考查比较全面，等差数列，等比数列的考查每年都不会遗漏。 有关数列的试题经常是综合题，经常把数列知识和指数函数、对数函数和不等式的知识综合起来，试题也常把等差数列、等比数列，求极限和数学归纳法综合在一起。 探索性问题是高考的热点，常在数列解答题中出现。本章中还蕴含着丰富的数学思想，在主观题中着重考查函数与方程、转化与化归、分类讨论等重要思想，以及配方法、换元法、待定系数法等基本数学方法。 近几年来，高考关于数列方面的命题主要有以下三个方面; (1)数列本身的有关知识，其中有等差数列与等比数列的概念、性质、通项公式及求和公式。 (2)数列与其它知识的结合，其中有数列与函数、方程、不等式、三角、几何的结合。 (3)数列的应用问题，其中主要是以增长率问题为主。 试题的难度有三个层次，小题大都以基础题为主，解答题大都以基础题和中档题为主，只有个别地方用数列与几何的综合与函数、不等式的综合作为最后一题难度较大。 知识整合 1、在掌握等差数列、等比数列的定义、性质、通项公式、前n项和公式的基础上，系统掌握解等差数列与等比数列综合题的规律，深化数学思想方法在解题实践中的指导作用，灵活地运用数列知识和方法解决数学和实际生活中的有关问题。 2、在解决综合题和探索性问题实践中加深对基础知识、基本技能和基本数学思想方法的认识，沟通各类知识的联系，形成更完整的知识网络，提高分析问题和解决问题的能力。 进一步培养学生阅读理解和创新能力，综合运用数学思想方法分析问题与解决问题的能力。 3、培养学生善于分析题意，富于联想，以适应新的背景，新的设问方式，提高学生用函数的思想、方程的思想研究数列问题的自觉性、培养学生主动探索的精神和科学理性的思维方法。
Mathematics Answering Skills in College Entrance Examination: Solutions to Series of Questions
Sequence problem is an important part of high school mathematics and the basis of learning higher mathematics. College Entrance Examination is a comprehensive examination of this chapter. The examination of equal-difference series and equal-ratio series will not be omitted every year. The questions about sequence of numbers are often comprehensive questions. They often combine the knowledge of sequence of numbers with the knowledge of exponential function, logarithmic function and inequality. They also integrate the sequence of equal difference and ratio, the method of seeking limit and mathematical induction. Exploratory questions are the hotspots of college entrance examination, often appearing in the series of answers. This chapter also contains a wealth of mathematical ideas, focusing on the main ideas of function and equation, transformation and transformation, classification and discussion, as well as basic mathematical methods such as formula method, exchange method, undetermined coefficient method. In recent years, the propositions of the college entrance examination on the number series mainly include the following three aspects: (1) the related knowledge of the number series itself, including the concept, nature, general term formula and summation formula of the equal difference series and the equal ratio series. (2) The combination of sequence and other knowledge, including sequence and function, equation, inequality, triangle and geometry. (3) The application of data series, in which the growth rate is the main problem. There are three levels of difficulty in the test questions. Most of the small questions are based on the basic questions. Most of the answers are based on the basic and intermediate questions. Only in some places, it is more difficult to use the synthesis of sequence and geometry, function and inequality as the last question. Knowledge integration 1. On the basis of mastering the definitions, properties, general term formulas, the first n terms and formulas of equal-difference series and equal-ratio series, we should systematically grasp the law of solving the comprehensive problems of equal-difference series and equal-ratio series, deepen the guiding role of mathematical thinking and methods in problem solving practice, and flexibly apply the knowledge and methods of equal-difference series to solve the relevant problems in mathematics and real life. 2. In the practice of solving comprehensive and exploratory problems, we should deepen our understanding of basic knowledge, basic skills and basic mathematical thinking and methods, communicate the connections of various kinds of knowledge, form a more complete knowledge network, and improve our ability to analyze and solve problems. Further develop students'reading comprehension and innovation ability, and comprehensively use mathematical thinking methods to analyze and solve problems. 3. To train students to be good at analyzing and associating questions so as to adapt to the new background and the new way of asking questions, to improve their consciousness of studying sequence problems with the thought of function and equation, and to cultivate students'spirit of active exploration and scientific and rational thinking methods.