In mathematics, a geometric progression, also known as a geometric sequence, is a sequence of non-zero numbers where each term after the first is found by multiplying the previous one by a fixed, non-zero number called the common ratio. For example, the sequence 2, 6, 18, 54, ... is a geometric progression with common ratio 3. Similarly 10, 5, 2.5, 1.25, ... is a geometric sequence with common ratio 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
[tex]{\displaystyle a,\ ar,\ ar^{2},\ ar^{3},\ ar^{4},\ \ldots }[/tex]
where r ≠ 0 is the common ratio and a ≠ 0 is a scale factor, equal to the sequence's start value.
The distinction between a progression and a series is that a progression is a sequence, whereas a series is a sum.
