NDA Mathematics Question (2025) — Solution

Step-by-step solution

For the first AP: 19, 21, 23, First term a_1 = 19, common difference d_1 = 2, number of terms n_1 = 110. Last term L_1 = a_1 + (n_1 - 1)d_1 = 19 + (110 - 1) 2 = 19 + 218 = 237. For the second AP: 19, 22, 25, 28, First term a_2 = 19, common difference d_2 = 3, number of terms n_2 = 75. Last term L_2 = a_2 + (n_2 - 1)d_2 = 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 (d_1, d_2) = LCM (2, 3) = 6. The last term of this new AP must be less than or equal to the smaller of the two last terms, which is (237, 241) = 237. Let the number of identical terms be n. a + (n - 1)D 237 19 + (n - 1) 6 237 6(n - 1) 218 n - 1 218 6 n - 1 36.33 n 37.33 Since n must be an integer, the maximum possible value for n is 37. Answer: 37