  A notion of n-Lie algebra introduced by V.T. Filippov can be viewed as a
generalization of a concept of binary Lie algebra to the algebras with n-ary
multiplication law. A notion of Lie algebra can be extended to Z_2-graded
structures giving a notion of Lie superalgebra. Analogously a notion of n-Lie
algebra can be extended to Z_2-graded structures by means of a graded Filippov
identity giving a notion of n-Lie superalgebra. We propose a classification of
low dimensional 3-Lie superalgebras. We show that given an n-Lie superalgebra
equipped with a supertrace one can construct the (n+1)-Lie superalgebra which
is referred to as the induced (n+1)-Lie superalgebra. A Clifford algebra
endowed with a Z_2-graded structure and a graded commutator can be viewed as
the Lie superalgebra. It is well known that this Lie superalgebra has a matrix
representation which allows to introduce a supertrace. We apply the method of
induced Lie superalgebras to a Clifford algebra to construct the 3-Lie
superalgebras and give their explicit description by ternary commutators.
