In this paper we investigate the global convergence result, boundedness and periodicity of solutions of the recursive sequence xn+1 = a0xn + a1xn−1 + . . . + akxn−k ⁄ b0xn + b1xn−1 + . . . + bkxn−k , n = 0, 1, . . . where the parameters ai and bi for i = 0, 1, . . . , k are positive real numbers and the initial conditions x−k, x−k+1, . . . , x0 are arbitrary positive numbers.