Geometric progression

A geometric progression, also known as a geometric sequence, is a mathematical sequence of non-zero numbers where each term after the first is found by multiplying the previous one by a fixed number called the common ratio. For example, the sequence 2, 6, 18, 54, ... is a geometric progression with a common ratio of 3. Similarly 10, 5, 2.5, 1.25, ... is a geometric sequence with a common ratio of 1/2.

Examples of a geometric sequence are powers r^k of a fixed non-zero number r, such as 2^k and 3^k. The general form of a geometric sequence is

${\displaystyle a,\ ar,\ ar^{2},\ ar^{3},\ ar^{4},\ \ldots }$

where r is the common ratio and a is the initial value.

The sum of a geometric progression's terms is called a geometric series.