How many terms are identical in the two APs 19, 21, 23, up to 110 terms and 19, 22, 25, 28, up to 75 terms?

Step-by-step solution

For the first AP: 19, 21, 23, First term a₁ = 19 , common difference d₁ = 2 , number of terms n₁ = 110 . Last term L₁ = a₁ + (n₁ - 1)d₁ = 19 + (110 - 1) 2 = 19 + 218 = 237 . For the second AP: 19, 22, 25, 28, First term a₂ = 19 , common difference d₂ = 3 , number of terms n₂ = 75 . Last term L₂ = a₂ + (n₂ - 1)d₂ = 19 + (75 - 1) 3 = 19 + 222 = 241 . The identical terms of both APs form a new AP. The first common term is a = 19 . The common difference of the new AP is D = LCM (d₁, d₂) = LCM (2, 3) = 6 . The last term