How many A.P.'s 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 no . of $A . P^{'} s = 3 \times 5 = 15.$

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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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