Explanation:
Geometric progression
In mathematics, a geometric progression, also known as a geometric sequence, is a sequence of numbers where each term after the
first is found by multiplying the previous one by a fixed non-zero number
called the common ratio. For example, the sequence 2, 6, 18, 54, ... is a geometric
progression with common ratio 3. Similarly 10, 5, 2.5, 1.25, ... is a geometric
sequence with common ratio 1/2. The sum of the terms of a geometric
progression is known as a geometric series.
Thus, the
general form of a geometric sequence is
and that of a geometric series is
where r ≠ 0 is the common ratio and a is a scale
factor, equal to the sequence's start value.
(Our solved example in mathguru.com uses
this concept)
Elementary
properties
The n-th term of a geometric
sequence with initial value a and common ratio r is
given by
Such a
geometric sequence also follows the recursive relation
for
every integer
Generally, to check whether a given
sequence is geometric, one simply checks whether successive entries in the
sequence all have the same ratio
The common ratio of a geometric series may
be negative, resulting in an alternating sequence, with numbers switching from
positive to negative and back. For instance
1, −3, 9, −27, 81, −243,
...
is a geometric sequence with common ratio
−3.
http://en.wikipedia.org/wiki/Geometric_progression
The
above explanation is copied from Wikipedia, the free encyclopedia and is
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License.