AMC 12 2009a 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 \textbf{(B)}\ \frac {1}{2} \textbf{(C)}\ 1 \textbf{(D)}\ \frac {1 + \sqrt {5}}{2} \textbf{(E)}\ 2