Sarah Bou L.
2 Answers By Expert Tutors
A geometric sequence is a sequence of numbers in which the ratio between consecutive terms is constant.
We can write a formula for the n th term of a geometric sequence in the form
a n = a r n ,
where r is the common ratio between successive terms.
Example 1:
{ 2 , 6 , 18 , 54 , 162 , 486 , 1458 , ... }
is a geometric sequence where each term is 3 times the previous term.
A formula for the n th term of the sequence is
a n = 2 3 ( 3 ) n
Example 2:
{ 12 , − 6 , 3 , − 3 2 , 3 4 , − 3 8 , 3 16 , ... }
is a geometric series where each term is − 1 2 times the previous term.
A formula for the n th term of this sequence is
a n = 24 ( − 1 2 ) n
Example 3:
{ 1 , 2 , 6 , 24 , 120 , 720 , 5040 , ... }
is not a geometric sequence. The first ratio is 2 1 = 2 , but the second ratio is 6 2 = 3 .
No formula of the form
a n = a r n can be written for this sequence.
See also arithmetic sequences .