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.

1, 3, 9, 27, …

64, –16, 4, –1, …

16, 24, 36, 54, …

1, 3, 9, 27, …
Since
Then a _{n} = 1(3 ^{n–1 })
Therefore, the eighth term of the sequence is

64, –16, 4, –1, …
Since
Then
Therefore, the eighth term of the sequence is

16, 24, 36, 54, …
Since
Then
Therefore, the eighth term of the sequence is