Write a java code to accept an integer array of user-defined length from the user. Then write methods to take care of the following tasks. Check your methods in the main method of your program (3 points). A method that finds the sum of the maximum value and the minimum value among all the elements of the array. (3 points)
Example: 10 15 4 19 2 12
The maximum value is 19 and the minimum value is 2. So the output should be 21.
A method that finds the largest gap between any two elements of the array. (4 points)
Example: 3 6 7 10
The largest gap can be found between 3 and 10 which is 10 - 3 = 7, hence the output 7.
A method that finds the Length of the Longest Arithmetic Progression in it. (5 points)
Example: 1 7 10 15 27 29
The Longest Arithmetic Progression in the array is {1, 15, 29}, and its length is 3, hence the out