Extrapolation methods to accelerate convergence of a sequence of iterates are investigated. A transformation formula derived from the related deterministic sequence is modified so that it may be used for the stochastic sequences. The S.E.R. method, which is related to Aitken's δ2 process, is discussed. For linearly convergent sequences it is shown that S.E.R. not only will converge if the original sequence converges, but will converge to the same limit. An analysis of the bounds for the convergence and the perturbations is made for Aitken's δ2 process, S.E.R. and S.E.O.R. The method is applicable to convergent and locally convergent vector sequences.