Revision as of 18:59, 17 January 2010 by imported>Peter Schmitt
A geometric sequence (or geometric progression) is a (finite or infinite) sequence
of (real or complex) numbers
such that the quotient (or ratio) of consecutive elements is the same for every pair.
In finance, compound interest generates a geometric sequence.
Examples
Examples for geometric sequences are
(finite, length 6: 6 elements, quotient 2)
(finite, length 4: 4 elements, quotient −2)
(infinite, quotient
)
Application in finance
The computation of compound interest leads to a geometric series:
When an initial amount A is deposited at an interest rate of p percent per time period
then the value An of the deposit after n time-periods is given by

i.e., the values
A=A0, A1, A2, A3, ...
form a geometric sequence with quotient q = 1+(p/100).
Mathematical notation
A finite sequence

or an infinite sequence

is called geometric sequence if

for all indices i. (The indices need not start at 0 or 1.)
General form
Thus, the elements of a geometric sequence can be written as

Sum
The sum (of the elements) of a finite geometric sequence is

The sum of an infinite geometric sequence is a geometric series:
