Formula for Summing up a Geometric Series with alternate addition and subtraction

Question

Is there a formula to figure of the sum of n terms of the following series where r is a constant.

$S = r^{n-1} - r^{n-2} + r^{n-3} - r^{n-4}\ldots r^0$

For $n=7$,

$S = r^6 - r^5 + r^4 - r^3 + r^2 - r^1 + r^0$

Answer 1

Hint: consider the ratio of the progression as being $-r$.