Sequence

Abstract

Also known as Geometric Progression, Geometric Sequence
A sequence is a list of numbers, each of which is called a term. Each term after the first is found by multiplying the previous term by a fixed, non-zero number called the common ratio
The nth term of a sequence is given by $a_{n} = a_{1} \cdot r^{(n - 1)}$ , where $a_{n}$ is the nth term, $a_{1}$ is the first term, $n$ is the term number, $r$ is the common ratio

Example

$1, - 2, 4, - 8, 16 \dots$ (common ratio: $- 2$ )

$- 5, 15, - 45, 135 \dots$ (common ratio: $- 3$ )

An arithmetic sequence is a list of numbers where the difference between any two consecutive terms is constant. This constant difference is called the common difference
The nth term of an arithmetic sequence is given by $a_{n} = a_{1} + (n - 1) d$ , where $a_{n}$ is the nth term, $a_{1}$ is the first term, $n$ is the term number, $d$ is the common difference

Example

$3, 7, 11, 15 \dots$ (common difference of $4$ )

$10, 5, 0, - 5 \dots$ (common difference of $- 5$ )