Let the two A.Ps be A.P1 and A.P2
For A.P1 the first term = a and the common difference = d
And for A.P2 the first term = b and the common difference = d
So, from the question we have
a100 – b100 = 100
(a + 99d) – (b + 99d) = 100
a – b = 100
Now, the difference between their 1000th terms is,
(a + 999d) – (b + 999d) = a – b = 100
Therefore, the difference between their 1000th terms is also 100.