Let A be the set of first 101 terms of an A.P., whose first term is 1 and the common difference is 5 and let B be the set of first 71 terms of an A.P., whose first term is 9 and the common difference is 7. Then the number of elements in A B , which are divisible by 3, is :

Step-by-step solution

The set A consists of the first 101 terms of an A.P. with first term a₁ = 1 and common difference d₁ = 5 . The terms of A are 1, 6, 11, 16, , 1 + (101-1) 5 = 501 . The set B consists of the first 71 terms of an A.P. with first term b₁ = 9 and common difference d₂ = 7 . The terms of B are 9, 16, 23, 30, , 9 + (71-1) 7 = 499 . The first common term of A and B is 16 . The common difference of the terms in A B is the least common multiple of d₁ and d₂ , which is lcm (5, 7) = 35 . The general term of A B is given by T_k