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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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