JEE Math Practice Question

If the coefficients of rth, (r+1)th, and (r + 2)th terms in the binomial expansion of $${{\rm{(1 + y )}}^m}$$ are in A.P., then m and r satisfy the equation

1. A.$${m^2} - m(4r - 1) + 4\,{r^2} - 2 = 0$$
2. B.$${m^2} - m(4r + 1) + 4\,{r^2} + 2 = 0$$
3. C.$${m^2} - m(4r + 1) + 4\,{r^2} - 2 = 0$$
4. D.$${m^2} - m(4r - 1) + 4\,{r^2} + 2 = 0$$