  The main purpose of this paper is to introduce the geometric difference
sequence space
  $l_\infty^{G} (\Delta_G)$ and prove that $l_\infty^{G} ({\Delta}_{G})$ is a
Banach space with respect to the norm $\left\|.\right\|^G_{{\Delta}_G}.$ Also
we compute the $\alpha$-dual, $\beta$-dual and $\gamma$-dual spaces. Finally we
obtain the Geometric Newton-Gregory interpolation formulae.
