Identify the common ratio of a geometric sequence, and find a given term and the sum of the first n terms.
Find the sum of an infinite geometric series, if it exists.
A sequence in which each term after the first is found by multiplying the preceding term by the same number is a geometric sequence.
Consider the sequence:
Note that multiplying each term by 3 produces the next term. We call the number 3 the common ratio because it can be found by dividing any term by the preceding term. A geometric sequence is also called a geometric progression.