Generalized symmetries, first integrals, and exact solutions of chains of differential equations

New integrability properties of a family sequences ordinary differential equations, which contains the Riccati and Abel chains as most simple sequences, are studied. The determination n generalized symmetries nth-order equation in each chain provides, without any kind integration, n-1 functionally independent first integrals equation. A remaining integral arises by quadrature using Jacobi last multiplier that is expressed terms preceding corresponding sequence. complete set used to obtain exact general solution results applied derive directly chains.