Research On The Number Sequence In Question Of High School Mathematics League

Since 1980,China mathematics education major competitions is mainly based on the National High School Mathematics League, and achieve long-term and stable development. There are some important knowledge is a "mid-compulsory, often often test new" in the league, which contains the problem of the Number Sequence. the Number Sequence has always been chosen as the test by Proposition group in the league. This paper attempts to Mathematical Competition for content research as a starting point, and focused on the the Number Sequence in question this particular test sites, through nearly 15 years. All series issues collected, explore the law, to front-line teachers, participants and even the proposition to provide some ideas and information.This paper is divided into five chapters, two parts. First, the development process of the National High School Mathematics League should be reviewed, including the change of the competition system and the question types, and then the proposition principles of the league is focused and summarized. The second part of the study is based on the first part, for the 2000--2015 National High School Mathematics League "series" questions are collected. Given the definition and property of the arithmetic and geometric sequence, and the "New Standard" for the number of columns as the early learning of foreshadowing. Then, from the macro and micro perspective of these questions have been studied.In the macro view,illustrates the evolving National Mathematics Competition to try and increase the types and test scores through the form type, and lists the number, the scores, the types and the knowledge points of each Number Sequence questions in nearly 15 years in the league. These data statistics through various angles, and gives the corresponding analysis charts, and summarizes the number of columns in the league of some of the problems of development characteristics. In the micro view, deep into the problem-solving process each question, and to questions over the years in the more typical examples of problem-solving ideas are classified research.The first category of questions is the general term questions by the number of recursive request. In Chapter 4, Section Iintroduces solving the most common fixed-point method, eigenvalue method, method of undetermined coefficients, mathematical induction and so on.The second category of questions is the number of columns summation problem. In Chapter IV, Section II gives the main way to solve such problems, including iterative method, Splitting Items Consumer Law and subtraction dislocation.The third category is using properties of sequences to solving problems. Number of columns many properties make it perfect in the exam can be flexible as a test point. Chapter IV, Section III gives the number of columns monotonicity, divisibility, infinite resistance, the boundedness definition of the starting point and purpose to do such practice, and the nature of the test series were classified to answer questions over the years.The fourth category is some comprehensive questions thatrelates to the sequence of number integrated with other knowledge points.Finally, combining with the above research summarized regularity and characteristics of the application, this paper gives a lesson plans about sequences of number question in National High School Mathematics League, in order to provide some reference and teaching thought for forefront educators.