Let S n denote the sum of the first n terms of an arithmetic progression. If S 10 = 390 and the ratio of the tenth and the fifth terms is 15 : 7 , then S 15 − S 5 is equal to:

Step-by-step solution

Given: a 10 a 5 = 15 7 ⇒ a + 9 d a + 4 d = 15 7 ⇒ 7 a + 63 d = 15 a + 60 d ⇒ 3 d = 8 a Also, S 10 = 390 ⇒ 10 2 2 a + 9 d = 390 ⇒ 2 a + 24 a = 78 ⇒ a = 3 ⇒ d = 8 ⇒ S 15 - S 5 = 15 2 6 + 14 × 8 - 5 2 6 + 4 × 8 ⇒ S 15 - S 5 = 15 2 × 118 - 5 2 × 38 ⇒ S 15 - S 5 = 885 - 95 ⇒ S 15 - S 5 = 790