For any nonnegative integer "k" and natural numbers "n" and "m," the equations presented in this paper demonstrate the inequalities obtained on the ratio for the geometric means of a positive arithmetic sequence with unit difference, where alpha epsilon [vertical bar]0,1[vertical bar] is a constant. Using the ideas and methods of Chen (2002), Kuang (1999), and Qi and Guo (2000), the author further generalizes these inequalities and obtains additional inequalities of the ratio for the geometric mean of a positive arithmetic sequence with unit difference and monotonicity results.