Question

consider the set s = (1 2 3 ??? 1000}. how many arithmetic progressions can be formed from the elements of s that start with 1 and end with 1000 and have at least 3 elements?

Answer 1

Here,d=common difference
(1)d=1
(2)d=2
(3)d=3
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(49)d=49
so,no. of A.P.s=49