  Let $(A,\m)$ be a Noetherian local ring with infinite residue field and let
$I$ be an ideal in $A$ and let $F(I) = \oplus_{n \geq 0}I^n/\m I^n$ be the
fiber-cone of $I$. We prove certain relations among the Hilbert coefficients of
$F(I)$ when the $a$-invariant of the associated graded ring $G(I)$ is negative.
