Basic Technical Mathematics, 11th Edition

19.2 Geometric Sequences

• Geometric Sequence • Common Ratio • Sum of n Terms

A second type of important sequence of numbers is the geometric sequence (or geometric progression). In a geometric sequence, each number after the first can be obtained from the preceding one by multiplying it by a fixed number, called the common ratio. We can express this definition in terms of the recursion formula

$$a_n\hspace{0.17em}=\hspace{0.17em}r{a}_{n\hspace{0.17em}-\hspace{0.17em}1}$$(19.4)

where $a_n$ is any term, $a_{n\hspace{0.17em}-\hspace{0.17em}1}$ is the preceding term, and r is the common ratio. One important application of geometric sequences is in computing compound interest on savings accounts. Other applications are found in areas such as biology and physics.

EXAMPLE 1 Illustrations of geometric sequences

1. The sequence 2, 4, 8, 16, …, is a geometric ...