When there is a common ratio (r) between consecutive terms, we can say this is a geometric sequence.
If the first term (T1) is a, the common ratio is r, and the general term is Tn, then:
Tn= ar n–1
Look at the sequence 5; 15; 45; 135; 405; …
Therefore, the common ratio is 3, and the sequence is geometric. To get the next term you multiply the preceding term by the common ratio.
Example 5:
Given the sequence 1; 2/3; 4/9; …
a) Determine the next two terms.
b) Which term of the sequence is equal to 32/243?
Solutions:
Example 6:
In a geometric sequence, the 5th term is 80 and the common ratio is –2. Determine the first three terms of the sequence.
