Cohen-Macaulayness of blow-ups of homogeneous weak d-sequences

Let R be a homogeneous Cohen-Macaulay algebra over a field, and let I be an ideal generated by a homogeneous weak d-sequence. We show, under reasonable conditions on the sequence, that the graded ring gr R[It] of the Rees algebra R[It]=⊕I is Cohen-Macaulay. In particular we obtain the Cohen-Macaulayness of the blow-up ring R[It]