We prove that every n-Jordan derivation in the sense of Herstein (Bull Am Math Soc 67:517-531, 1961, p. 528) on n!-torsion free unital commutative rings is a derivation. Furthermore, we prove that every continuous n-Jordan derivation on semiprime normed algebras is a derivation. The results of this paper improve and generalize the main results of Bridges and Bergen (Proc Am Math Soc 90:25–29, 1984), but under weaker assumptions. Some applications and examples of our results are also provided
