We have investigated spin dynamics of both the ladder and the chain sites in Sr₁₄Cu₂₄O₄₁ by Cu-NMR and Cu-NQR. From the NMR shift, K_spin and nuclear spin-lattice relaxation time, T₁, the energy gaps in the spin excitation spectrum are confirmed to be Δ=140 K for the chain site and Δ=470 K for the ladder site for Sr₁₄Cu₂₄O₄₁. Doping effects on the spin gaps and electric field gradient at the Cu sites were also investigated by the substituting of Ca, Y and La for Sr. The spin gap of the ladder site decreases with increasing x for Sr_14-xCa_xCu₂₄O₄₁ and seems to collapse at around x=13 for Ca substitution.