Sequences and Progressions — Introduced Through Examples

A sequence is simply a list of numbers written in a definite order, following some rule — for example $2, 4, 6, 8, \ldots$ or $1, 3, 9, 27, \ldots$. Each number in the list is called a term, and the terms are written $T_1, T_2, T_3, \ldots$ (or sometimes $a_1, a_2, a_3, \ldots$), where $T_n$ denotes the $n$-th term.

Two particular kinds of sequence appear constantly in business and commercial arithmetic — instalment schedules, depreciation, population and sales growth, compound interest — and this chapter studies both:

Look at how differently the two sequences grow: the AP $3,7,11,15,19,\ldots$ increases by the same amount every step, while the GP $2,6,18,54,162,\ldots$ grows faster and faster because each step multiplies by the same factor. Recognising which pattern a given list of numbers follows — a constant difference or a constant ratio — is the first skill this chapter builds, before moving on to formulas for a general term and for sums.

This WBCHSE Class 11 Business Mathematics and Basic Statistics chapter covers Arithmetic and Geometric Progressions exactly as prescribed in the West Bengal HS commerce mathematics syllabus — the same AP/GP techniques (general term, sum to $n$ terms) that also underpin instalment and annuity calculations studied later in the course.