Calculation of arithmetic force

1. The ratio increasing method and the equal difference increasing method are two methods to calculate the rent in the leasing business. According to its basic formula, we can dece and calculate that if the rent is calculated and paid according to the equal proportion increasing method, the actual rent rate will drop, or even drop by a large margin, resulting in the loss of the interests of the lessor; If the rent is calculated according to the equal difference increasing method, the actual rent rate is always equal to the nominal rent rate, and the calculation is simple. Therefore, the equal difference increasing method is more fair, reasonable and practical than the equal ratio increasing method. With the deepening of the teaching reform in middle schools in China, the mathematics curriculum standard for primary and secondary schools in Shanghai (Trial draft) proposes to vigorously promote the digital mathematics activity (Dima) based on modern information technology, and establish the digital mathematics activity (Dima) with computers and calculators (including scientific calculators Function calculator and graphic calculator) as the support, has intelligent software and rich courseware, connection information network Dima platform. Using this platform, we can improve the processing and presentation of mathematics content, and let students learn independently in the information technology environment, and carry out experiments, exploration and research. In vigorously promoting the universal application of information technology in the teaching process, and promoting the integration of information technology and subject curriculum today, our school is also implementing curriculum reform, and the graphic calculator is also applied to the classroom of mathematics expansion course. For this reason, we designed a teaching case of "using graphic calculator to study several methods of expressing arithmetic and proportional sequence". 1、 Teaching background: in the chapter "sequence", when explaining the concepts of arithmetic sequence and proportional sequence, the content is relatively simple and easy for students to master. It is the basis of learning sequence, which is helpful to cultivate students' observation ability and inction ability. The contents of the equal ratio sequence and the equal difference sequence are completely parallel, including the definition, the nature, the formula of the general term, the equal ratio (difference) median of two numbers, etc. After more than half a year's study on the use of graphic calculators, senior one students have a preliminary understanding of the use of graphic calculators to analyze, construct and explore mathematical problems. They felt that the use of graphic calculator not only changed their way of learning mathematics, but also increased their interest in learning mathematics. They like this "do math" way of learning very much. Graphic calculator has many functions of using sequence, such as the use of general formula and recursive formula of sequence, the function of sequence image and image tracking, the expression function of sequence operation table, the iteration function of sequence and the programming function of sequence. All these have played a great role in learning the basic knowledge of sequence, correctly understanding sequence, making students experience the cognitive process of formula, understand the mathematical thinking method, and improve the ability of problem-solving in the effective attempt to guess, reasonable inction, simplified operation and verification operation. 2、 The design idea of the lesson is that the core of the whole series knowledge learning is the two conventional series of equal difference series and equal ratio series. Conjecture, inction, recursion, analogy and other mathematical ideas are fully reflected in the learning of these two basic knowledge, which can be described as "although a sparrow is small, it has all five internal organs". However, it is difficult to fully and correctly show these in the traditional sequence teaching. This will lead to students' one-sided understanding of what they have learned, which will have a negative impact on the follow-up study of sequence. The graphic calculator has many functions to use the sequence, such as the use of the general formula and recursive formula, the image and image tracking function, the expression function of the operation table, the iteration function and the programming function of the sequence. All these have played a great role in learning the basic knowledge of sequence, correctly understanding sequence, making students experience the cognitive process of formula, understand the mathematical thinking method, and improve the ability of problem-solving in the effective attempt to guess, reasonable inction, simplified operation and verification operation. Therefore, we envisage that students can have a clear understanding of the two conventional series by studying and expressing the series with graphic calculator. At the same time, we also want to cultivate students' initiative and inquiry spirit and improve their mathematics learning ability through this learning process. Design and Implementation: the teaching content of the new textbook pays more attention to the integration of function thought and computer technology. From the beginning of this chapter, the textbook puts the number sequence in the context of function and gives the definition: the number sequence is a function with a positive integer set (or its finite subset) as the domain of definition. When the independent variable values in the order from small to large, the corresponding function value is the term of the number sequence. Sequence is a kind of discrete function. In the allocation of exercises, teaching materials are often compared with function teaching. The general term formula, recurrence formula and image of arithmetic sequence and proportional sequence are the main contents of our research in this lesson. We imagine that with the help of graphic calculator, we can make students have a vivid, comprehensive and correct understanding of sequence knowledge by doing mathematics, so as to improve students' mathematical thinking ability and cultivate students' correct mathematical view, Really improve students' interest in mathematics learning. Case 1 (1) find the 11th term of the arithmetic sequence - 121, - 110, - 99, - 88,... (2) write the general term formula and recurrence formula of the sequence. For this problem, we can calculate the result according to its basic law. But using graphic calculator can make us think about the solution of the problem from many angles, which is concive to students' comprehensive and correct understanding of the characteristics of arithmetic sequence, so as to simplify the calculation. Method 1: use the iteration function of numerical value (as shown in Figure 1): Method 2: use the array function of graphic calculator (as shown in Figure 2): Method 3

3. Summation formula: (a1 + an) * n / 2
general formula: an = a1 + n * D

4. It's very simple. I didn't learn what I just learned today. However, it is difficult to follow the sequence. Formula: an = a1 + {n-1} D

6. Strange question, you are talking about the last term.
arithmetic sequence {an}
first term
A1
, tolerance
d
nth term
an =
a1 + (n-1) d
if you know
AK and tolerance
d
A1 = AK - (k-1) d

7.

Indefinite integral result is not unique, derivative verification should be able to improve the calculation ability of the differential

It is enough to master the arithmetic sequence

8. Equal ratio: the proct of the former and the latter is equal to the square of the middle term
equal difference: the sum of the former and the latter is equal to twice of the middle term

9. First minus last divided by number of items