Geometric Sequence

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. 1, 3, 9, 27, …
  2. 64, –16, 4, –1, …
  3. 16, 24, 36, 54, …
  4. 1, 3, 9, 27, …
  5. Since
  6. Then a n= 1(3 n–1 ) Therefore, the eighth term of the sequence is 
  7. 64, –16, 4, –1, …
  8. Since
  9. Then
  10. Therefore, the eighth term of the sequence is 
  11. 16, 24, 36, 54, …
  12. Since
  13. Then
  14. Therefore, the eighth term of the sequence is 
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