  The catenary degree is an invariant that measures the distance between
factorizations of elements within a numerical semigroup. In general, all
possible catenary degrees of the elements of the numerical semigroups occur as
the catenary degree of one of its Betti elements. In this study, Betti elements
of some telescopic numerical semigroup families with embedding dimension three
were found and formulated. Then, with the help of these formulas, Frobenius
numbers and genus of these families were obtained. Also, the catenary degrees
of telescopic numerical semigroups were found with the help of factorizations
of Betti elements of these semigroups
