Foundational Math: Arithmetic and Geometric Sequences and Series

Sequences and series are fundamental mathematical tools used to model predictable patterns of growth, change, and iteration across various scientific and financial applications. This course provides a solid, text-based foundation in the two most common types: arithmetic and geometric progressions. By the end of this course, you will be able to confidently analyze patterned data, derive general formulas for specific terms, and calculate the total sum of a series, preparing you for advanced algebra and calculus topics. What you'll learn: * Understand the core definitions and key differences between arithmetic and geometric sequences. * Apply the necessary formulas to find the $n$th term of any sequence based on its common difference or ratio. * Calculate the finite sum of both arithmetic and geometric series using summation notation. * Analyze infinite geometric series and determine whether they converge to a finite sum. * Practice applying sequences and series concepts to solve realistic modeling problems involving compound growth and decay. The course begins with terminology and notation, moves step-by-step through deriving and applying the core formulas, and concludes with extensive practice problems designed to solidify your understanding. This course is designed for absolute beginners in mathematics or those needing a thorough refresher on foundational algebra; no prior knowledge of sequences or series is required. Start building your mathematical modeling skills today.