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

Application of Geometric Calculus in Numerical Analysis and Difference Sequence Spaces