5.5 Geometric sequence:

A geometric sequence is a sequence in which the ratio of any term to the previous term is constant. The explicit formula for a geometric sequence is of the form a n = a 1^r-1, where r is the common ratio. A geometric sequence can be defined recursively by the formulas a 1 = c, a_n+1 = ra_n , where c is a constant and r is the common ratio.

The sum of a finite geometric sequence (the value of a geometric series) can be found according to a simple formula. For a geometric sequence a_n = a 1 r_n-1, the sum of the first n terms is

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