Pre-Calculus For Dummies
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When your pre-calculus teacher asks you to find the partial sum of a geometric sequence, the sum will have an upper limit and a lower limit. The common ratio of partial sums of this type has no specific restrictions.

You can find the partial sum of a geometric sequence, which has the general explicit expression of


by using the following formula:


For example, to find


follow these steps:

  1. Find a1 by plugging in 1 for n.

  2. Find a2 by plugging in 2 for n.

  3. Divide a2 by a1 to find r.

    For this example, r = –3/9 = –1/3. Notice that this value is the same as the fraction in the parentheses.

    You may have noticed that 9(–1/3)n – 1 follows the general formula for


    (the general formula for a geometric sequence) exactly, where a1 = 9 and r = –1/3. However, if you didn't notice it, the method used in Steps 1–3 works to a tee.

  4. Plug a1, r, and k into the sum formula.

    The problem now boils down to the following simplifications:


    Geometric summation problems take quite a bit of work with fractions, so make sure to find a common denominator, invert, and multiply when necessary. Or you can use a calculator and then reconvert to a fraction. Just be careful to use correct parentheses when entering the numbers.

About This Article

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About the book author:

Mary Jane Sterling taught algebra, business calculus, geometry, and finite mathematics at Bradley University in Peoria, Illinois, for more than 30 years. She is the author of several For Dummies books, including Algebra Workbook For Dummies, Algebra II For Dummies, and Algebra II Workbook For Dummies.

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