•A geometric sequence is one in which the ratio of successive terms is constant. In other words, each number in the sequence is multiplied by a constant number to obtain the next number in the sequence:
–A basic example of a geometric sequence is 1, 2, 4, 8, 16, …
Consider a geometric sequence in which the general terms are a1, a2, a3, …
In order to determine the ratio r of successive terms, simply use the formula r = an+1/an.
In general, the formula for the nth term of a geometric sequence is an = a1 rn-1.
–Example: Consider the sequence: 1, 3, 9, 27, … Find the 6th term of the sequence:
Notice that in this geometric sequence the ratio r = 9/3 = 3.
Also note that a1 = 1 and n = 6.
Therefore, a6 = 1 (3)6-1 = 35 = 243.