In this paper, we examine the accelerated expansion of the Universe in the
    framework of $f\left( Q\right) $ gravity theory in which the non-metricity
    scalar $Q$ describes the gravitational interaction. To find the exact solutions
    to the field equations in the FLRW Universe, we propose a new parametrization
    of the Hubble parameter and we estimate the best fit values of the model
    parameters by using the combined datasets of updated $H(z)$ consisting of $57$
    points, the Pantheon consisting of $1048$ points, and BAO datasets consisting
    of six points with the Markov Chain Monte Carlo (MCMC) method. The evolution of
    deceleration parameter indicates a transition from the deceleration to the
    acceleration phase of the Universe. In addition, we investigate the behavior of
    statefinder analysis and Om diagnostic parameter, Further, to discuss other
    cosmological parameters, we consider two $f\left( Q\right) $\ models,
    specifically, $f\left( Q\right) =\lambda Q$ and $f\left( Q\right) =Q+mQ^{n}$,
    where $\lambda $, $m$ and $n$ are free parameters. Lastly, we found that both
    $f(Q)$ models predict that the present Universe is accelerating and the EoS
    parameter behaves like the quintessence model.



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