If the n^ th common term of the arithmetic progressions 2, 7, 12, 17, and 1, 4, 7, 10, is 322 , then the value of n is equal to

Step-by-step solution

Let the first arithmetic progression be S₁ = 2, 7, 12, 17, The first term of S₁ is a₁ = 2 and its common difference is d₁ = 5 . Let the second arithmetic progression be S₂ = 1, 4, 7, 10, 13, 16, 19, The first term of S₂ is a₂ = 1 and its common difference is d₂ = 3 . By observing the terms of both progressions, the first common term is A = 7 . The sequence of common terms will also form an arithmetic progression. Its common difference D is the least common multiple of d₁ and d₂ . D = LCM (5, 3) = 15 . The n^ th com