A sequence is defined as a set of real numbers with a natural order. A sequence is usually included in brackets ({}), with the terms, or parts of a sequence, separated by commas. For example, if a scientist collects weather data every day for many days, the first day of collecting can be written as x₁ data; then x₂ for the second day, and so on until x_n, in which n is the eventual number of days. This can be written as {x₁, x₂, … x_n} _n≥1. In general, the sequence of numbers in which x_n is the nth number is written using the following notation: {x_n}_n≥1.

A sequence can get larger or smaller. For example, in the sequence for {2ⁿ}_n≥1, the solution is 2 ≤ 4 ≤ 8 ≤ 16 ≤ 32, and so on, with the numbers getting larger. Whereas, for {1/n}_n≥1, the sequence becomes 1 ≥ ½ ≥ 1/3 ≥ 1/4 ≥ 1/5, and so on, with the numbers getting progressively smaller. This does not mean that sequences only get progressively larger and smaller; certain solutions for sequences include a mix of the two.