Let C be a
suitable triangulated category with a Serre functor and an
n-cluster tilting subcategory T= add(t), for some integer
n>1. In this setup, every indecomposable in T appears in a so
called Auslander-Reiten (n+2)-angle in T. We show that the
Grothendieck group of C can be expressed as a quotient of the
split Grothendieck group of T by some elements determined by the
Auslander-Reiten (n+2)-angles in T. We also apply this result to
an example.