In this paper, we study the least number L ∈ N that makes the L-fold of a weighted r-generalized Fibonacci power complete. We can establish an upper bound and a lower bound for L, depending on the first r terms and the limit of the consecutive ratios. We also give the explicit value of L in some special cases. In the end, we study a particular minimal complete sequence called a generalized distinguished sequence and show that there exists a generalized distinguished sequence of a weighted r-generalized Fibonacci mth power for all large m ∈ N.