smc

Given first term $a$ and common ratio $r$, we have $a=a\ast r+a\ast r^2$, and. We divide by $a$ in the first equation to get $1=r+r^2$. Rewriting, we have $r^2+r-1=0$. We use the quadratic formula to get $r=\frac{-1+-\sqrt{1^2-4(1)(-1)}}{2(1)}$. Because the terms all have to be positive, we must add the discriminant, getting an answer of $\frac{\sqrt{5}-1}{2}$ $\boxed{\frac{\sqrt{5}-1}{2}}$.