Four series of ternary rare-earth zinc arsenides have been prepared by reaction of the elements at 750 C: RE4Zn2-xAs5 forming for RE = La-Nd, Sm; and RE5Zn2-xAs6, RE6Zn2-xAs7, RE7Zn2-xAs8 forming for RE = Ce, Pr, Nd, Sm. They crystallize in trigonal structure types in space group P (3) over bar m1 with Z = 1 for RE4Zn2-xAs5 and RE7Zn2-xAs8, or space group R (3) over bar m1. with Z = 3 for RE5Zn2-xAs6 and RE6Zn2-xAs7. Through the structural principle of intergrowing rocicsalt-type [REM] slabs of variable thickness within a parent CaAl2Si2-type structure containing Zn-deficient [Zn2-xAs2] slabs built from edge-sharing Zn-centered tetrahedra, these ternary arsenides belong to a homologous series with the formulation REZn2-xAs2 center dot n(REAs) (n = 3, 4, 5, 6). Quaternary derivatives Ce-4(Mn,Zn)(2-x)As-5 and Ce-6(Mn,Zn)(2-x)As-7 were also obtained in which Mn partially substitutes for Zn. Band structure calculations predict that the electronic properties can be gradually modified from semiconducting to semimetallic behavior as more [REAs] slabs are introduced.