Let 3 , 7 , 11 , 15 , . . , 403 and 2 , 5 , 8 , 11 , . . . , 404 be two arithmetic progressions. Then the sum, of the common terms in them, is equal to_________

Step-by-step solution

Given AP are: 3 , 7 , 11 , 15 , . . , 403 and 2 , 5 , 8 , 11 , . . . , 404 a 1 = 3 , a 2 = 2 , d 1 = 4 , d 2 = 3 So, for the common AP, a = 11 , d = LCM 3 , 4 = 12 Also, a n ≤ 403 ⇒ 11 + n - 1 12 ≤ 403 ⇒ - 1 + 12 n ≤ 403 ⇒ n ≤ 404 12 ⇒ n ≤ 33 . 6 ⇒ n = 33 ⇒ S n = 33 2 2 × 11 + 32 × 12 ⇒ S n = 6699