In a typical Calculus 2 class, sequences and series are learned near the end of the semester. In my Calculus 2 class in Spring 2020, we started with polynomial approximations to functions on day 1 of class. Why?
Constructing a sequence of functions (in this case, polynomials) that converge to a function is one of the most important ideas in analysis.
Polynomial approximations to functions introduce and provide context for sequences and series.