The Sum of a Finite Geometric Sequence

The sum of the finite geometric sequence Image with common ratio r≠1 is given by Image.

PROOF: By beginning with the equation for the sum of all terms of a finite geometric sequence  Image , we can multiply each side of the equation by to obtain the equation:Image.

Subtracting the second equation from the first and then factoring yields Image, and, because r≠1, we haveImage.