smc

Using the formula for the sum of a geometric series we get that the sums of the given two sequences are $\frac{a}{1-r_1}$ and $\frac{a}{1-r_2}$. Hence we have $\frac{a}{1-r_1}=r_1$ and $\frac{a}{1-r_2}=r_2$. This can be rewritten as $r_1(1-r_1)=r_2(1-r_2)=a$. As we are given that $r_1$ and $r_2$ are distinct, these must be precisely the two roots of the equation $x^2-x+a=0$. Using Vieta's formulas we get that the sum of these two roots is $\boxed{1}$.