  Approximation sequences and derived equivalences occur frequently in the
research of mutation of tilting objects in representation theory, algebraic
geometry and noncommutative geometry. In this paper, we introduce symmetric
approximation sequences in additive categories and weakly $n$-angulated
categories which include (higher) Auslander-Reiten sequences (triangles) and
mutation sequences in algebra and geometry,and show that such sequences always
give rise to derived equivalences between the quotient rings of endomorphism
rings of objects in the sequences modulo some ghost and coghost ideals.
