sequence
A sequence is an ordered list of numbers, like beads strung on a wire in a fixed order: a first bead, a second, a third, and so on. The order matters — 1, 2, 3 is a different sequence from 3, 2, 1 — and usually the numbers follow some pattern you can describe.
Each number in the list is called a term, and its position is given by a whole-number index, often written with a subscript: a_1 is the first term, a_2 the second, a_n the n-th. A sequence can be finite (it stops) or infinite (it goes on forever, written with an ellipsis like 2, 4, 6, 8, ...).
Formally a sequence is just a function whose inputs are the positive integers (or sometimes the non-negative integers): you feed it a position n and it returns the term a_n. That viewpoint is why every sequence can, in principle, be described by a formula in n.
The squares form the sequence 1, 4, 9, 16, 25, ... with a_n = n^2, so a_4 = 16.
A sequence given by an explicit formula in its position n.
Do not confuse a sequence (the ordered list) with a series (the sum of that list). The sequence 1, 2, 3 lists three numbers; the corresponding series is 1 + 2 + 3 = 6.