Answer :

Two arithmetic progressions have the same common difference.

Let, common difference = d


First term of first A.P. = a


First term of second A.P. = a’


Given that difference between their 100th term is 100


100th term of first A.P., a100 = a + 99d


100th term of second A.P., a’100 = a’ + 99d


Acc. To question,


a100 – a’100 = 100


a + 99d – a’ – 99d = 100


a – a’ = 100 (i)


1000th term of first A.P., a1000 = a + 999d


1000th term of second A.P., a’1000 = a’ + 999d


Acc. To question,


a1000 – a’1000 = a + 999d – a’ – 999d


= a – a’


a1000 – a’1000 = 100 [from (i)]


Hence, difference between 1000th term of two A.P. is 100


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