ARITHMETIC PROGRESSIONS (ОБРАЗОВАНИЕ НАУКА И ИННОВАЦИОННЫЕ ИДЕИ В МИРЕ, 2025)
This article discusses arithmetic progressions (AP), a fundamental topic in mathematics that appears in both theoretical and practical contexts. Arithmetic progression is a sequence of numbers in which each term after the first is obtained by adding a fixed number, called the common difference. The paper explores the definition, properties, and formulas associated with arithmetic progressions, including the nth term and the sum of the first n terms. Illustrative examples and real-life applications are provided to enhance understanding. The pedagogical importance of teaching AP in secondary and higher education is highlighted, emphasizing its role in problem-solving and preparation for advanced mathematical concepts. The article concludes by underlining the significance of arithmetic progressions in fostering logical reasoning and analytical thinking.