11.3 Geometric Sequences and Series

  • 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.

Geometric Sequences

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.

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