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Use of the Geometric Mean Return Formula. The formula for the geometric mean return is used specifically for investments that are compounded. By contrast, a simple interest account would use the arithmetic average which is summing the rates and dividing by the number of periods.
Common ratio[edit] The convergence of the geometric series with r=1/2 and a=1/2. The convergence of the geometric series with r=1/4 and a=1. The terms of a geometric series form a geometric progression, meaning that the ratio of successive terms in the series is constant. This relationship allows for the representation of a geometric series using only two terms, r and a. The term r is the common ratio, and a is the first term of the series.