Can you make sure to write the recursive function and not the program please and thank you in advance.

1. Write a recursive function (not the program) that returns the sum of the cubes of the positive integers from 0 to n, where n is a positive integer. (15 points) 2. Write a recursive function (not the program) that returns true if the digits of a positive integer are in increasing order; otherwise, the function returns false. (15 points) 3. Write a recursive function that uses an array parameter to accept integers and returns the average of the integers stored in the array. Assume that the size of the array be n. (20 points) 4. Write a recursive function (not the program) to find sum and product of the following: (30 points) a) Sum = 15+30+45+60+75+90+105+120+135+150+165+180+195+210+225 b) Product=2*3*5*7*9*11*13*17*19*23*29*31*37*41 5. Write a recursive function that gets an integer as a parameter and returns the pattern as shown below. For example, if user passes an input integer 3 to the function, it should output (20 points) *** *** *** **