  We use the Lie group analysis method to investigate the invariance properties
and the solutions of \begin{align*} x_{n+1} =\frac{x_{n-5}x_{n-3}}{x_{n-1}(a_n
+b_nx_{n-5}x_{n-3})}. \end{align*} We show that this equation has a
two-dimensional Lie algebra and that its solutions can be presented in a
unified manner. Besides presenting solutions of the recursive sequence above
where $(a_n)$ and $(b_n)$ are sequences of real numbers, some specific cases
are emphasized.
