How to Use Arithmetic Sequence Formulas and Calculate Partial Sums

The Organic Chemistry Tutor

This educational video provides a comprehensive tutorial on the fundamental formulas associated with arithmetic sequences and series. The narrator begins by defining an arithmetic sequence as a list of numbers with a common difference and demonstrates how to identify patterns using specific examples. The video methodically breaks down the notation used in algebra, distinguishing between term position (n) and term value (a_n), and explains the concept of a common difference (d). The core of the video focuses on deriving and applying essential algebraic formulas. It introduces the standard nth term formula, explores variations that allow calculation from any starting term (not just the first), and explains the concept of the arithmetic mean (the average of terms). The latter part of the video shifts to arithmetic series, explaining the difference between sequences and series, and teaching how to calculate partial sums using both long-hand addition and the summation formula. This resource is highly valuable for high school algebra and pre-calculus classrooms. It clarifies common points of confusion, such as the difference between a term's value and the sum of a series up to that term. The step-by-step problem-solving approach makes it an excellent tool for introducing new concepts or reviewing for exams. Teachers can use this video to scaffold learning, moving from basic pattern recognition to complex summation notation (sigma).