In this work we investigate the effect of the symmetry in a 2-D arrays of gold nanoparticle on the sensitivity to the refractive index change. We demonstrate a generalized result that an asymmetric periodic arrangement of metallic nanoparticle leads to a higher sensitivity than a regular square of nanoparticle. Further decreasing the symmetry of the system by using asymmetric nanoparticle (nanorods, triangle) rather than symmetric nanoparticle (nanocylinder) will further improve this sensitivity. Finally, we suggest that such asymmetric nanostructure could operate as a SERS and LSPR plasmon based sensor by changing the polarization of the incident light.