Recovering $\Lambda$CDM Model From a Cosmographic Study
  Using the mathematical definitions of deceleration and jerk parameters we
obtain a general differential equation for squared Hubble parameter. For a
constant jerk, this differential equation leads to an exact function for Hubble
parameter. By the aid of this exact Hubble function we can exactly reconstruct
any other cosmographic parameters. We also obtained a general function for
transition redshift as well as spacetime curvature. Our derived functions
clearly impose a lower limit on the jerk parameter which is
$j_{min}\geq-0.125$. Moreover, we found that the jerk parameter indicates the
geometry of the spacetime i.e any deviation from $j=1$ imply to a non-flat
spacetime. In other word $j\neq 1$ reefers to a dynamical, time varying, dark
energy. From obtained Hubble function we recover the analogue of $\Lambda$CDM
model. To constrain cosmographic parameters as well as transition redshift and
spacetime curvature of the recovered $\Lambda$CDM model, we used
Metropolis-Hasting algorithm to perform Monte Carlo Markov Chain analysis by
using observational Hubble data obtained from cosmic chronometric (CC)
technique, BAO data, Pantheon compilation of Supernovae type Ia, and their
joint combination. The only free parameters are $H$, $A(\Omega_{m})$ and $j$.
From joint analysis we obtained $H_{0}=69.9\pm 1.7$,
$A(\sim\Omega_{0m})=0.279^{+0.013}_{-0.017}$,
$B(\sim\Omega_{0X})=0.721^{+0.017}_{-0.013}$, $j_{0}=1.038^{+0.061}_{-0.023}$
and $z_{t}=0.706^{+0.031}_{-0.034}$.
