ARITHMETIC PROGRESSION

Abstract

An arithmetic progression (AP) is a sequence of numbers where the difference between any two consecutive terms is constant, known as the common difference (d). The sequence is defined by its first term (a) and the common difference. The general formula for the \( n \)-th term of an AP is \( a_n = a + (n-1)d \). The sum of the first \( n \) terms (\( S_n \)) can be calculated using \( S_n = \frac{n}{2} (2a + (n-1)d) \) or \( S_n = \frac{n}{2} (a + l) \), where \( l \) is the last term. APs are widely used in various fields such as finance, physics, engineering, and computer science, due to their regular and predictable nature.