Mastering Arithmetic and Geometric Sequences and Series

The Organic Chemistry Tutor

This comprehensive math tutorial provides a deep dive into arithmetic and geometric sequences and series, fundamental concepts in high school algebra and pre-calculus. The video begins by clearly distinguishing between the two types of sequences: arithmetic sequences, defined by a common difference (addition/subtraction), and geometric sequences, defined by a common ratio (multiplication/division). It breaks down the essential formulas for finding the nth term, calculating arithmetic and geometric means, and determining partial sums for both types of series. The tutorial progresses from basic definitions to more complex applications, covering the distinction between finite and infinite sequences, as well as the difference between a sequence (a list of numbers) and a series (the sum of those numbers). It introduces both explicit and recursive formulas, showing students how to generate terms from a rule and conversely, how to derive a general rule from a list of numbers. Special attention is given to fractional sequences and identifying patterns that are neither purely arithmetic nor geometric. Designed for the classroom, this video is packed with practice problems that reinforce learning. It walks through identifying pattern types, calculating specific terms like the 10th or 50th term, and finding sums of large sets, such as the first 300 natural numbers or all even numbers between 2 and 100. This resource is an excellent tool for teachers to use for direct instruction, review, or as a flipped classroom assignment for students in Algebra 2 or Pre-Calculus courses.