The refractive index sensitivities of plane Ag nanosphere cluster sensors (dimer, trimer, pentamer and heptamer) are numerically investigated by finite element method. Their localized surface plasmon resonance wavelengths λLSPR and sensitivity factors ΔλLSPR/Δnm are shown to increase quadratically and linearly with the refractive index of surrounding mediums (nm, varying from 1 to 2), with the same quadratic and linear coefficients, respectively. The corresponding mechanisms are elucidated in terms of the linear response of Ag optical constant within the concerned visible range. The electromagnetic coupling between component NSPs are interestingly revealed to not affect such quadraticity and linearity.