A geometric sequence is a set of ordered numbers for which the ratio of successive terms is the same.
In a geometric sequence, the first term is multiplied by a number called the common ratio to create the second term which is multiplied by the common ratio to create the third term and so on.
The common ratio, or , is calculated as follows:
Like in arithmetic sequences, the first term is denoted by .
To find whether a sequence is geometric, all terms must be tested for a common ratio. This is calculated as follows:
Which of the following are geometric sequences?
Check that the ratio is the same.
There is a common ratio of 4. Therefore this is a geometric sequence where and .
Check that there is a common ratio.
There is a common ratio of -2. Therefore this is a geometric sequence where and .
There is not a common ratio so this is not a geometric sequence.
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