2009 AMC 12A Problem 17

Let a + ar_1 + ar_1^2 + ar_1^3 + \cdots and a + ar_2 + ar_2^2 + ar_2^3 + \cdots be two different infinite geometric series of positive numbers with the same first term. The sum of the first series is r_1, and the sum of the second series is r_2. What is r_1 + r_2?

\textbf{(A)}\ 0\qquad \textbf{(B)}\ \frac {1}{2}\qquad \textbf{(C)}\ 1\qquad \textbf{(D)}\ \frac {1 + \sqrt {5}}{2}\qquad \textbf{(E)}\ 2

Full credit goes to MAA for authoring these problems. These problems were taken on the AOPS website.