THE SIGNIFICANCE OF AN ARITHMETIC PROGRESSION AS A MATHEMATICAL MODEL
Keywords:
Arithmetic progression; linear change; mathematical modeling; constant difference; prediction; data analysis; linear functions; Gauss; Euler; Descartes; economic forecasting; educational mathematics; decision-making; real-life applications.Abstract
Arithmetic progression (AP) represents one of the most fundamental mathematical models used to describe linear change in real-life contexts. Its structure, defined by a constant difference between consecutive terms, enables the accurate modeling of uniform growth and decline in natural, economic, and social processes. This paper explores the significance of AP as a versatile analytical tool, highlighting its ability to predict future values, simplify data interpretation, and form the conceptual basis for linear mathematical models. Insights from classical mathematicians such as Gauss, Euler, and Descartes, as well as modern scholars in economics, education, and applied sciences, demonstrate the wide applicability of AP in forecasting, planning, and decision-making. The study concludes that arithmetic progression is not only an essential element of mathematical theory but also a practical and reliable instrument for understanding and managing linear patterns in everyday life.
References
1. Euler L. Introductio in analysin infinitorum. — Lausanne : Bousquet, 1748. — 2 v.
2. Gauss C. F. Disquisitiones Arithmeticae. — Leipzig : Gerhard Fleischer, 1801. — 472 p.
3. Descartes R. La Géométrie. — Leiden : Ian Maire, 1637. — 412 p
4. Pólya G. How to Solve It: A New Aspect of Mathematical Method. — Princeton : Princeton University Press, 1945. — 253 p.
5. Pólya G. Mathematics and Plausible Reasoning. Vol. 1: Induction and Analogy in Mathematics. — Princeton : Princeton University Press, 1954. — 280 p.
6. Skemp R. R. The Psychology of Learning Mathematics. — London : Penguin Books, 1971. — 256 p.
7. Bruner J. S. The Process of Education. — Cambridge, MA : Harvard University Press, 1960. — 176 p.
8. Vygotsky L. S. Mind in Society: The Development of Higher Psychological Processes. — Cambridge, MA : Harvard University Press, 1978. — 159 p.
9. Bloom B. S. Taxonomy of Educational Objectives. Handbook I: Cognitive Domain. — New York : David McKay, 1956. — 207 p.
