Primes in general arithmetical progressions

Effective mathematics learning is a significant challenge in improving students' understanding and skills in mathematical concepts. One exciting approach to enhancing mathematics education is Realistic Mathematics Education (RME), which emphasizes understanding mathematical concepts through real-world contexts. This research combines the RME approach with Augmented Reality (AR) technology to facilitate the learning of sequences and arithmetic series. This research aims to create a learning trajectory that can help students understand the concept of arithmetic sequences and series using the context of the Borobudur Temple in grade 8th of SMP Negeri 4 Semarang. This research uses a design research method which consists of three stages, namely preliminary design, design experiment (pilot experiment and teaching experiment), and retrospective analysis. In this research, a series of learning activities were designed and developed based on the RME approach. This research involved 6 grade 8th students. The result of this research is a learning trajectory that includes a series of learning processes in three activities, namely: 1) Observing Borobudur Temple videos to understand the definition and characteristics of sequences and series; 2) finding the formulas and results of sequences and series; 3) and solving contextual problems related to sequences and series. The activities carried out can help improve students' understanding of the sequences and arithmetic series material. The research results show that the context of the Borobudur Temple can help students understand the concept of sequences and arithmetic series. Apart from that, the results of this research add options for local wisdom that can be used as a context for mathematics learning, especially sequences, and arithmetic series.

This research aims to determine: (1) students' difficulties in understanding the concept of arithmetic sequences and series, (2) students' difficulties in applying the principles of arithmetic sequences and series in solving problems, and (3) students' difficulties in finding information contained in sequences and arithmetic series questions. arithmetic series using the Make a Match learning model in class XI IPS 1 SMA NEGRI 8 Padangsidimpuan. The research carried out was qualitative research using qualitative descriptive methods. The subjects in this research were students of class XI IPS 1 SMA NEGRI 8 PADANGSIDIMPUAN. Data collection techniques by means of interviews with tests.The results of the research showed that the 4 students who were interviewed and completed the test questions found that the four students had different difficulties in solving sequence and series story questions. In understanding concepts, students who have difficulty will find it difficult to understand the concept of arithmetic sequences and series and will not be able to apply it to story problems for arithmetic sequences and series. When finding the information contained in the problem, students who experience difficulty will find it difficult to find the information and convert the mathematical information into the form of a mathematical model so they will experience difficulty in determining principles or formulas if the information contained in the story is not known beforehand.

This research aims to solve everyday life problems using the concept of arithmetic sequences and series. The type of research used is qualitative research. The type of data used is secondary data. Data collection method uses library research. The method for this study uses previous literature studies, books and journals. An arithmetic sequence is a number that has a certain pattern and a fixed difference. while an arithmetic series is the sum of all the numbers in the arithmetic series. The concept of arithmetic sequences and series can be applied in life as a solution to solve everyday life problems.

Problems that are often faced to prove the truth of a formula if the presented series is a series that is not the formula of arithmetic and geometric series. One proof among the most commonly proofs used is the proof by mathematical induction. This study was conducted to determine the sum of the first n terms formula of: (1) arithmetic series, storied arithmetic series with the basis of arithmetic series, (2) geometric series, (3) storied arithmetic series with the basis of geometric series, and (4) series which are not arithmetic and geometric series that the formula of the n terms is given, by using the finite difference method and Newton's theorem. The formula of the sum of the first n terms obtained from the results of this study and then it is verified by using mathematical induction. Keywords : Series, finite difference, mathematical induction, Newton’s theorem

This research aims to solve everyday life problems using the concept of arithmetic sequences and series. The type of research used is qualitative research. The type of data used is secondary data. Data collection method uses library research. The method for this study uses previous literature studies, books and journals. An arithmetic sequence is a number that has a certain pattern and a fixed difference. while an arithmetic series is the sum of all the numbers in the arithmetic series. The concept of arithmetic sequences and series can be applied in life as a solution to solve everyday life problems.

We study triangles and cyclic quadrilaterals which have rational area and whose sides form geometric or arithmetic progressions. A complete characterisation is given for the infinite family of triangles with sides in arithmetic progression. We show that there are no triangles with sides in geometric progression. We also show that apart from the square there are no cyclic quadrilaterals whose sides form either a geometric or an arithmetic progression. The solution of both quadrilateral cases involves searching for rational points on certain elliptic curves.

Research in learning media development is driven by the common problem of student disengagement, which hinders their understanding of the material. The specific problem addressed in this research is students' lack of attention and comprehension while studying arithmetic sequences and series. The purpose of this study is to document the process and outcomes of developing interactive learning media using Articulate Storyline specifically for the material on sequences and arithmetic series. The research follows the Research and Development (R&D) approach, employing the Thiagarajan model (Model 4-D) consisting of four stages: 1) the definition stage (define), 2) the design stage (design), 3) the development stage (development), and 4) the dissemination stage (disseminate). The research was conducted with a sample of 31 students from class X B at SMA Tunas Luhur. The results of the media validity test showed a score of 4.82, indicating high validity. Furthermore, the practicality and effectiveness tests conducted with both small and large groups achieved a perfect score of 100% in all aspects. This research indicates that the interactive learning media for arithmetic sequences and series based on Articulate Storyline meet the criteria of validity, practicality, and effectiveness.

Present paper envisages a novel approach to explore some real sequences by using the gamma function, arithmetic progression (AP) and geometric progression (GP). Particularly, applications of properties of both the arithmetic progression (AP) and geometric progression (GP) are focused to find out some real sequences which can be significantly useful in emerging fields of engineering science and technology. Real sequences play vital role in testing of convergence of infinite power series in real analysis and engineering mathematics. In this paper, several propositions pertaining to real sequences are explored and examined by way of presenting proofs. In addition to this, various numerical examples are also illustrated in order to emphasis the application aspect of real sequences explored herein. Finally, some significant conclusions are drawn for future scope and further findings with different versions of real sequences.

Background: The lack of learning media based on Computational Thinking (CT) for high school students, especially in the material arithmetic sequences and series, is one of the causes of students' low CT skills.Aim: This research was conducted to develop learning media in the form of Electronic Student Worksheets on the material of arithmetic series and sequences to improve CT skills by utilizing Liveworksheets media.Method: This research was conducted using a design research method, a development study type with the Tessmer development model. The focus is on the development of CT-based Electronic Student Worksheets.Result: The validation value of the developed CT-based Electronic Student Worksheets reached 95.47%, while the practicality assessment of CT-based Electronic Student Worksheets based on the questionnaire obtained a value of 89.97%Conclusion: Based on the results of the study, it can be concluded that the developed CT-based Electronic Student Worksheets meets the valid and practical criteria to be used in learning to improve CT skills and understanding of arithmetic sequences and series material for high school students.

The development of the world of education in Indonesia can not be separated from the influence of globalization, science and technology are always growing rapidly give a comprehensive impact on all aspects of human life, including the sector of education. Resilient and competitive human resources are needed to meet these challenges. Thus, the need to know about Adversity Quotient of a person to know how far a person can survive and overcome the difficulty. Mathematics which is a universal science underlies the development of modern technology and has an important role in various disciplines. The development of problem-solving abilities is also one of the most important aspects in the objectives of mathematics learning, especially on sequence materials and arithmetic series. Arithmetic sequences and series became a very important mathematical concept because of its wide application, so widely used in daily life. So this qualitative research is done with the aim to describe the process of solving the problem of rows and arithmetic series of junior high school students based on Adversity Quotient climber category. Technique of data collection is done by giving of Problem Solving Task (TPM) sequence and arithmetic series and job-based interview. Based on the analysis of research data that has been done, it is concluded that climber students in understanding the problem trend to read the problem twice. In plotting problem solving, climber students have an alternative solution to solve a given problem. At the implementation stage, climber students solve existing problems based on the most appropriate appropriate problem-solving plan and clearly disclose the truth information from the solution of the problem that has been done. The process of re-examining the problem solving, it is clear that the climber's students are re-checking and also trying to find alternative ways to solve the problem by first making an illustration of the drawing before doing the calculation process.
 
 Key Word: Problem Solving, Arithmetic Sequences and Series, Climber

In this article we investigate when the set of primitive geodesic lengths on a Riemannian manifold have arbitrarily long arithmetic progressions. We prove that in the space of negatively curved metrics, a metric having such arithmetic progressions is quite rare. We introduce almost arithmetic progressions, a coarsification of arithmetic progressions, and prove that every negatively curved, closed Riemannian manifold has arbitrarily long almost arithmetic progressions in its primitive length spectrum. Concerning genuine arithmetic progressions, we prove that every noncompact, locally symmetric, arithmetic manifold has arbitrarily long arithmetic progressions in its primitive length spectrum. We end with a conjectural characterization of arithmeticity in terms of arithmetic progressions in the primitive length spectrum. We also suggest an approach to a well known spectral rigidity problem based on the scarcity of manifolds with arithmetic progressions.

Effects of school and classroom characteristics on pupil progress in language and arithmetic

Discrepancy in generalized arithmetic progressions

Properness of nilprogressions and the persistence of polynomial growth of given degree

Research Article| January 01 2008 "In Arithmetical Progression": Shaw, Wells, and Fitzgerald THOMAS D. BIRCH THOMAS D. BIRCH Search for other works by this author on: This Site Google The F. Scott Fitzgerald Review (2008) 6 (1): 55–68. https://doi.org/10.2307/41583128 Cite Icon Cite Share Icon Share Twitter Permissions Search Site Citation THOMAS D. BIRCH; "In Arithmetical Progression": Shaw, Wells, and Fitzgerald. The F. Scott Fitzgerald Review 1 January 2008; 6 (1): 55–68. doi: https://doi.org/10.2307/41583128 Download citation file: Zotero Reference Manager EasyBib Bookends Mendeley Papers EndNote RefWorks BibTex toolbar search Search Dropdown Menu toolbar search search input Search input auto suggest filter your search All Scholarly Publishing CollectivePenn State University PressThe F. Scott Fitzgerald Review Search Advanced Search The text of this article is only available as a PDF. Copyright © 2008 The F. Scott Fitzgerald Society/Wiley Periodicals, Inc.2008The F. Scott Fitzgerald Society/Wiley Periodicals, Inc. Article PDF first page preview Close Modal You do not currently have access to this content.