The Geometric progression reference article from the English Wikipedia on 24-Apr-2004 (provided by Fixed Reference: snapshots of Wikipedia from wikipedia.org)

Geometric progression

In mathematics, a geometric progression is a sequence of numbers such that the quotient of any two successive members of the sequence is a constant. For instance, the sequence 3, 6, 12, 24, 48, ... is a geometric progression with common quotient 2. A geometric progression has exponential growth (or decay).

If the initial term of a geometric progression is a and the common quotient of successive members is r, then the n-th term of the sequence is given by a rⁿ,  n = 0, 1, 2, ...

The sum of the numbers in a geometric progression is called a geometric series. A convenient formula for geometric series is available:

Compare this with a arithmetic progression showing linear growth (or decline) such as 4, 15, 26, 37, 48, .... Note that the two kinds of progression are related: taking the logarithm of each term in a geometric progression yields an arithmetic one.

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