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We consider the random walk in an independent and identically distributed(i.i.d.) random environment on a Cayley graph of a finite free product ofcopies of $\mathbb{Z}$ and $\mathbb{Z}_2$. Such a Cayley graph is readily seento be a regular tree. Under a uniform elipticity assumption on the i.i.d.environment we show that the walk has positive speed and establish the annealedcentral limit theorem for the graph distance of the walker from the startingpoint.

S.L.L.N. and C.L.T. for Random Walks in I.I.D. Random Environment on Cayley Trees