jmc

Let the common ratio of the first sequence be $p$ and the common ratio of the second sequence be $r$. Then the equation becomes

$$k{p}^2-k{r}^2=2(kp-kr)$$Dividing both sides by $k$ (since the sequences are nonconstant, no term can be $0$), we get

$$p^2-r^2=2(p-r)$$The left side factors as $(p-r)(p+r)$. Since $p\ne r$, we can divide by $p-r$ to get

$$p+r=\boxed{2}$$