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A sequential procedure is developed to construct a fixed accuracy confidence interval (CI) of the common unknown variance of the random observations, where the observations arise from a first-order stationary autoregressive (AR(1)) process with a continuous and symmetric error distribution having mean zero and finite fourth-order moment. Using relevant estimators of the parameter of interest, related asymptotic properties of the derived fixed accuracy confidence interval are worked out. Furthermore, empirical evaluation of the proposed procedure together with application of it in the context of a real data is provided.