On the difference equation ${ x_{n+1}=\frac{ax_{n}^{2}+bx_{n-1}x_{n-k}}{cx_{n}^{2}+dx_{n-1}x_{n-k}}} - Elabbasy, E. M.; El-Metwally, H.; Elsayed, E.M. (Sarajevo journal of mathematics, 2024)
In this paper we investigate the global convergence result, boundedness, and periodicity of solutions of the recursive sequence \begin{equation*}x_{n+1}=\frac{ax_{n}^{2}+bx_{n-1}x_{n-k}}{cx_{n}^{2}+dx_{n-1}x_{n-k}},\;\;\;n=0,1,…\end{equation*}where the parameters $a,b,c$ and $d$ are positive real numbers and the initial conditions $ x_{-k},x_{-k+1},…,x_{-1}$ and $x_{0}$ are arbitrary positive numbers.