This section provides step-by-step examples on how to analyze ordered lists of numbers. You will learn to find specific terms and sums of arithmetic and geometric sequences, evaluate infinite series, and expand binomials using the Binomial Theorem.

An arithmetic progression has a constant common difference ($d$) between consecutive terms. The $n$-th term is $a_n = a_1 + (n - 1)d$.

A geometric progression has a constant common ratio ($r$) between consecutive terms. The $n$-th term is $a_n = a_1 \cdot r^{n-1}$.

A sequence is in harmonic progression if the reciprocals of its terms form an arithmetic progression. To solve problems involving HPs, convert the terms to their reciprocals, solve as an AP, and then invert the result.

The Binomial Theorem is a method for expanding expressions of the form $(a + b)^n$ without doing manual multiplication.