Final answer:
The index range for accessing elements of the 'grades' array in the program segment is 0 to 49, with the index starting at 0 for the first element and ending at 49 for the last element.
Step-by-step explanation:
The index range capable of accessing an element of the grades array is (A) 0..49. In the program segment provided, grades = new double[50]; declares an array of double variables with 50 elements. Since array indexing in Java starts at 0, the first element has an index of 0 and the last element has an index of the size of the array minus one, which in this case is 49.