We investigate the magnetic properties of the Cu-O planes in stoichiometric Sr n− 1 Cu n+ 1 O 2 n (n= 3, 5, 7,...) which consist of CuO double chains periodically intergrown within the CuO 2 planes. The double chains break up the two-dimensional antiferromagnetic planes into Heisenberg spin ladders with n r= 1/2 (n-1) rungs and n l= 1/2 (n+ 1) legs and described by the usual antiferromagnetic coupling J inside each ladder and a weak and frustrated interladder coupling J’. The resulting lattice is a new two-dimensional trellis lattice. We first examine the spin excitation spectra of isolated quasi-one-dimensional Heisenberg ladders which exhibit a gapless spectrum when n r is even and n l is odd (corresponding to n= 5, 9,...) and a gapped spectrum when n r is odd and n l is even (corresponding to n= 3, 7,...). We use the bond operator representation of quantum S= 1/2 spins in a mean-field treatment with self-energy corrections and obtain a spin gap of≊ 1/2J for the simplest single-rung ladder (n= 3), in agreement with numerical estimates. We also present results of the dynamical structure factor S (q, ω). The spin gap decreases considerably on increasing the width of the ladders. For a double ladder with four legs and three rungs (n= 7) we obtain a spin gap of only 0.1 J. However, a frustrated coupling, such as that of a trellis lattice, introduced between the double ladders leads to an enhancement of the gap. Thus stoichiometric Sr n− 1 Cu n+ 1 O 2 n compounds with n= 3, 7, 11,..., will be frustrated quantum antiferromagnets with a quantum-disordered or spin-liquid ground state.