Revision as of 12:38, 9 January 2010 by imported>Peter Schmitt
A geometric sequence is a (finite or infinite) sequence
of (real or complex) numbers
such that the quotient of consecutive elements is the same for every pair.
Examples for geometric sequences are
- (finite, length 6: 6 elements, quotient 2)
- (finite, length 4: 4 elements, quotient −2)
- (infinite, quotient )
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: