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
-
