Mathematical Analysis

Sequences and Series

What is a geometric sequence?

A geometric sequence—or geometric progression—is a finite or infinite sequence of real numbers with the ratio between two consecutive terms being constant (called the common ratio or r); in this case, each term is the previous term multiplied by a given number. In a geometric sequence, the formula for the nth term, in terms of the first number and the common ratio, becomes:

The first term is a1, r is the common ratio, and the number of terms is n. For example, for the numbers 2, 6, 18, 54, 162, a1 is 2, r is 3, and n is 5. The equation then becomes:


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