How to Find the First Four Terms of a Sequence

The Organic Chemistry Tutor

This educational video provides a clear, step-by-step tutorial on how to generate the first four terms of a mathematical sequence given an explicit formula. The narrator demonstrates the process of substitution, replacing the variable 'n' with integers 1, 2, 3, and 4 to calculate specific terms. Two distinct examples are provided: a linear equation that results in an arithmetic sequence and a quadratic equation that results in a non-arithmetic sequence. The video explores key themes such as functional notation, substitution, pattern recognition, and the definition of arithmetic sequences. It explicitly contrasts a sequence with a constant common difference against one where the difference between terms changes, helping students understand the defining characteristics of linear versus non-linear growth patterns. For educators, this video serves as an excellent direct instruction tool or review resource for Algebra units covering sequences and series. It breaks down the abstract notation of $a_n$ into concrete arithmetic steps, making it accessible for students struggling with function notation. The clear visual contrast between the two examples allows teachers to segue into deeper discussions about linear functions, slope, and quadratic growth.