A geometric sequence is a sequence in which each term is found by multiplying the preceding term by the same value. Its general term is
a n = a 1 r n – 1
The value r is called the common ratio. It is found by taking any term in the sequence and dividing it by its preceding term.
Example 1
Find the common ratio in each of the following geometric sequences. Then express each sequence in the form a n = a 1 r n – 1 and find the eighth term of the sequence.
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1, 3, 9, 27, …
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64, –16, 4, –1, …
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16, 24, 36, 54, …
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1, 3, 9, 27, …
Since 
Then a n = 1(3 n–1 )
Therefore, the eighth term of the sequence is
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64, –16, 4, –1, …
Since 
Then 
Therefore, the eighth term of the sequence is
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16, 24, 36, 54, …
Since 
Then 
Therefore, the eighth term of the sequence is
