The truncated sequential probability ratio test of two simple hypotheses is considered for the model of independent non-identically distributed observations. The lower and upper bounds are given for the probability that the necessary number of observations to stop the test does not exceed a preassigned number. New inequalities for the error probabilities of type I and II are obtained to generalize the classic results. New approximations for the error probabilities of type I and II are constructed. The results are applied for the model of time series with trend. In addition, properties of a sequential test based on the least squares method parameter estimate at the moment of truncation are analyzed for the model of time series with trend. Computer experiment results are given.