Abstract
This paper aims to develop a new method to obtain periodic solutions with period two and three of the following recursive sequence
x(n+1) = alpha + beta x(n)/x(n-1) + gamma x(n-1)/x(n),
where the parameters alpha, beta and gamma are positive real numbers and the initial conditions x(-1), x(0) are positive real numbers. Also, it investigates the global convergence and boundedness of the aforementioned equation.