The sum of $$n$$ consecutive integers is 0 ; we need to check that which of the given options is true.

For the sum of consecutive integers to be 0 , we would have to consider the integers of the form $2 a +1$ , where a integers are negative, a integers are positive (same as those negative) \& one is zero. For example the set $$-3,-2,-1,0,1,2,3$$ has sum 0 , if we increase a negative element in the list, the same element will be added with positive sign also.

Now checking from the options, we have

(A) n is odd integer, which is true as the number of integers must be of the form $$2 \mathrm{a}+1$$, where a is any non negative integer
(B) $$n$$ is even integer - false
(C) the median of the numbers must be 0 - which is true as the middle term of the set must be 0 .
(D) the average of the numbers is equal to the median - which is true as in case of consecutive integers, the average must be equal to the median.

Hence options (A), (C) \& (D) are true.