ARITHMETIC PROGRESSION

Abdurashitov Rakhmatullo Abdukhamitovich; Khusenov Zikrillo Raxmatillo ogli; Adkhamov Khasanboy Abdusalom ogli

Authors

Abdurashitov Rakhmatullo Abdukhamitovich
Khusenov Zikrillo Raxmatillo ogli
Adkhamov Khasanboy Abdusalom ogli

Keywords:

Arithmetic progression, common difference, first term, (n)-th term(a_n), sequence, linear sequence, uniform difference, incremental change, mathematical series, geometric progression, algorithm, signal processing.

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.