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    Geometric Sequences


    Geometric sequences possesses the simple recursion formula:
    an = ran-1

    where r is a fixed number known as the common ratio
    Sum of the First n Terms
    For geometric sequence {an} with first term a1 and common ratio r (r ≠ 0, r ≠ 1), the following applies for every positive integer n:



    Example:

    Find the sum of the first ten terms of the geometric sequence:  3,          −6, 12, −24, ....

     Solution:




    Sum of Infinte Geometric Series

    For geometric sequence {an} with first term a1 and common ratio r (|r| < 1), the following applies



    Examples: