Of course you remembered to initialize sum to zero,
as below:
Here is a complete program that includes the new method. All the previous methods of the class can be included where the comment indicates.
class ArrayOps
{
  // . . . previous methods go here 
  // add up all the elements in an array
  int sumElements ( int[] nums )
  {
    int sum = 0;
    for ( int j=0; j < nums.length; j++  )
      sum += nums[j];
    return  sum;
  }
}
class ArrayDemo
{
  public static void main ( String[] args ) 
  {
    ArrayOps operate = new ArrayOps();
    int[] ar1 =  { -20, 19, 1, 5, -1, 27, 19, 5 } ;
 
    System.out.println("The sum of elements is: " + 
      operate.sumElements( ar1 ) );   
  }
}
Notice how the main() method uses the method call
as if it were a number:
System.out.println("The sum of elements is: " + 
  operate.sumElements( ar1 ) );   
  --------------------------
             55
The method call returns the value 55 (the sum of all the array elements). That value can be used just as if it had been written there as a constant.
Would the following statement be correct as part of main()?
int value = operate.sumElements( ar1 ) / 4 + 32;