Let 3 , 6 , 9 , 12 , … upto 78 terms and 5 , 9 , 13 , 17 , … upto 59 terms be two series. Then, the sum of the terms common to both the series is equal to ______.

Step-by-step solution

Given, 3 , 6 , 9 , ⋯ upto 78 terms ⇒ t 78 = 3 + 77 × 3 = 234 5 , 9 , 13 , ⋯ upto 59 terms ⇒ t 59 = 5 + 58 × 4 = 237 Common difference of common terms = LCM 3 , 4 = 12 First common term is 9 and last common term is 225 So series will be 9 , 21 , 33 , ⋯ , 225 ⇒ n = 19 S = n 2 a + l = 19 2 9 + 225 = 2223