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MnBi_2+2nTe_4+3n are promising topological insulators (TI) where the natural intergrowth of magnetic layers and TI layers provides a unique platform for the study of interplay between magnetism and topological electronic states. Here we present our inelastic neutron scattering (INS) study on single crystals MnBi₂Te₄ and MnBi₄Te₇. We find that antiferromagnetic (AF) interlayer magnetic interactions in MnBi₂Te₄ which are vanishingly small in MnBi₄Te₇, need to be anisotropic for a consistent description of both INS and magnetization measurements. The modeling of two-dimensional intralayer ferromagnetic (FM) spin waves requires introduction of long-range and competing FM and AF magnetic interactions up to the seventh nearest neighbor. First principles calculations of insulating MnBi₂Te₄ support this model. The abnormal spin wave peak widths observed with INS could result from Mn vacancies/ Mn-Bi anti-site exchange as suggested by our spin dynamics simulation.