How to Calculate the Sum of a Geometric Series

By Chad Stetson; Updated April 24, 2017
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A geometric series is a sequence of numbers created by multiplying each term by a fixed number to get the next term. For example, the series 1, 2, 4, 8, 16, 32 is a geometric series because it involves multiplying each term by 2 to get the next term. In mathematics, you may need to find the sum of the geometric series. You can do this by using a simple formula.

Understand the formula. The formula for determining the sum of a geometric series is as follows: Sn = a1(1 - r^n) / 1 - r. In this equation, "Sn" is the sum of the geometric series, "a1" is the first term in the series, "n" is the number of terms and "r" is the ratio by which the terms increase. In the example series 2, 4, 8, 16, 32, you know that a1 = 2, n = 5 and r = 2.

Plug in the known variables to the equation. To determine the sum, it is necessary to know the exact values of "a1," "n" and "r." Sometimes you will already know these values and other times you will have to determine them by simply counting. For example, you may be given the series 2, 4, 8, 16, 32, or you may be given the series 2, 4, 8 ... and told that "n" = 5. It is therefore not necessary to know every term in the series. When you know the values of the three variables, plug them in. In the example, this would give you: Sn = 2(1 - 2^5) / 1 - 2.

Simplify the equation. Because you have all the needed information, you can simplify the equation to determine the geometric sum. You don't need to use any of the algebraic methods to move variables around because your "Sn" value is already isolated. Follow the basic order of simplifying an equation: brackets, exponents, multiplying/division and then addition/subtraction. In the example given, you will get: 2(-31) / -1, which further simplifies to 62. If the geometric series is simple -- like the example -- you can double-check your work: 2 + 4 + 8 + 16 + 32 = 62. The geometric sum is correct.