In this paper we investigate the global convergence result, boundedness, and periodicity of solutions of the recursive sequence $$x_{n+1}=\dfrac{\alpha x_{n-l}+\beta x_{n-k}}{Ax_{n-l}+Bx_{n-k}},\quad n=0,1,\dots$$ where the parameters $\alpha,\beta, A$ and $B$ are positive real numbers and the initial conditions $x_{-p}, x_{-p+1},\dots,x_{-1}$ and $x_0\in (0,\infty)$ where $p = \max\{l, k\}$.