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Concept

Geometric Sequence

A geometric sequence is a sequence in which the ratio between consecutive terms is a nonzero constant. This ratio is called the common ratio. The following is an example geometric sequence with first term and common ratio
Geometric Sequence: 3, 6, 12, 24, 48, ... with a common ratio of 2
The behavior of geometric sequences generally depends on the values of the first term and the common ratio The following table shows the effects of these parameters.
Increasing
Decreasing
Constant

Constant

Decreasing
Increasing
Alternating

Alternating

Like for any other sequence, the first term of a geometric sequence is denoted by the second by and so on. Since geometric sequences have a common ratio once one term is known, the next term can always be found by multiplying the known term by

General geometric sequence a_1, a_2, a_3, a_4, a_5, ... with a common ratio of r.

In fact, the sequence can be found using only and since all the subsequent terms can be found by multiplying by a specific number of times. Because of this, geometric sequences have the following general form.