Sequences are ordered lists of elements
Definition: a sequence is a function from a subset of integers (usually either set $\{0, 1, 2, ..\}$ or $\{1, 2, 3, …\}$) to a set $S$
The notation $a_n$ denotes the image of the integer $n$. We can think of $a_n$ as the equialent of $f(n)$, where $f$ is a function from $\{0, 1, 2, …\}$ to $S$
We call $a_n$ a term of the sequence
Defintion: a geometric progression is a sequence of the form: $a, ar, ar^2, ar^3, …, ar^n, ..$ where the initial term $a$ and the common ratio $r$ are real numbers
Definition: an arithmetic progression is a sequence of the form: $a, a+d, a+2d, …, a+dn, …$ where the initial term $a$ and the common difference $d$ are real numbers.
Definition: a recurrence relation for the sequence $\{a_n\}$ is an equation that expresses $a_n$ in terms of one or more of the previous terms of the sequence, namely, $a_0, a_1, …, a_{n-1},$ for all integers $n$ with $n ≥ n_0$, where $n_0$ is a nonnegative integer.