Let a is the first term and d is the common difference of the AP

Given 9th term of AP = 499

=> a + 8d = 499 .....1

Again 499th term of AP = 9

=> a + 498d = 9 .....2

Now subtractct equation 1 and 2, we get

      a + 8d - (a + 498d) = 499 - 9

=> a + 8d - a - 498d = 499 - 9

=> -490d = 490

=> d = -490/490

=> d = -1

Put value of d in equation1, we get

      a - 8 = 499

=> a = 499+8

=> a = 507

Let nth term is equal is to zero

=> a + (n-1)d = 0

=> 507 - (n-1) = 0         (By putting value of a and d)

=> 507 - n +1 = 0

=> 508 - n = 0

=> n = 508

So 508th term of AP is equal to zero.