## Summary/Background

A geometric progression, also known as a geometric sequence, is a sequence of 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 and 10, 5, 2.5, 1.25, ... is a geometric sequence with common ratio 1/2.

The sum of the terms of a geometric progression is known as a geometric series.

\displaystyle \sum_{k=1}^n ar^{k-1} = ar^0 + ar^1 + ar^2 + ... + ar^{n-1}

The sum of the terms of a geometric progression is known as a geometric series.

\displaystyle \sum_{k=1}^n ar^{k-1} = ar^0 + ar^1 + ar^2 + ... + ar^{n-1}

## Software/Applets used on this page

## Glossary

### geometric

A sequence where each term is obtained by multiplying the previous one by a constant.

### sequence

a number pattern in a definite order following a certain rule

### series

the sum of terms in a sequence

### union

The union of two sets A and B is the set containing all the elements of A and B.