Two arithmetic progressions have the same common difference. The difference between their 100th terms is 100, what is the difference between their 1000th terms?

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


27