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

an = ran − 1(19.4)

where an is any term, an − 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 ...

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