Geometric sequence: Difference between revisions
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Again, <math>a_1</math> is the first term in the sequence, and <math>r</math> is the common ratio. | Again, <math>a_1</math> is the first term in the sequence, and <math>r</math> is the common ratio. | ||
==Also | ==See Also== | ||
[[arithmetic sequence|Arithmetic Sequences]] | [[arithmetic sequence|Arithmetic Sequences]] | ||
Revision as of 01:01, 23 June 2006
Definition
A geometric sequence is a sequence of numbers where the nth term of the sequence is a multiple of the previous term. For example: 1, 2, 4, 8, 16, 32, ... is a geometric sequence because each term is twice the previous term. In this case, 2 is called the common ratio of the sequence.
Summing a Geometric Sequence
The sum of the first 
terms of a geometric sequence is given by
where 
is the first term in the sequence, and 
is the common ratio.
Infinate Geometric Sequences
An infinate geometric sequence is a geometric sequence with an infinate number of terms. These sequences can have sums, sometimes called limits, if 
.
For instance, the series 
, sums to 2. The general fromula for the sum of such a sequence is:
Again, is the first term in the sequence, and is the common ratio.
