how many ap with 10 terms are there whose first term is in the set {1,2,3} and whose common difference is in the set {1,2,3,4,5}

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Solution

There are 3 ways to choose the first term and corresponding to each such way there are 5 ways of selecting the common difference.
So, required number of A.P's
= 3×5 = 15.

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