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Geometric progression (view source)
Revision as of 01:31, January 20, 2007
, 01:31, January 20, 2007Compound interest as an example of a geometrical progression; exponential growth
A geometric progression is a sequence of numbers that has a constant ratio of each term to its preceding term. For example, this is a geometric progression: 2, 4, 8, 16, 32.
A geometric progression is a sequence of numbers that has a constant ratio of each term to its preceding term. For example, this is a geometric progression: 2, 4, 8, 16, 32.
In finance, [[compound interest]] is an example of a geometric progression. An example would be a bank account that earns an API (annual percentage interest) rate of 5% per year. Every year, the number of dollars in the account is multiplied by the factor 1.05. That is about the same as doubling every fifteen years.
The sequence 2, 4, 8, 16, 32 is simply the "powers of two:" two, two squared, two cubed, two to the fourth power, and so on. This can be written using ''exponents'' this way:
::2<sup>1</sup>, 2<sup>2</sup>, 2<sup>4</sup>, 2<sup>8</sup>, 2<sup>16</sup>, 2<sup>32</sup>.
This is why geometric progressions are sometimes called "exponential growth."