The sum of four numbers in an arithmetic progression is 48 and the ratio of the product of the extremes to the product of the two middle terms is 27 : 35 , then the largest term of this arithmetic progression is

Step-by-step solution

Let the A. P. be a - 3 d ,   a - d ,   a + d ,   a + 3 d The sum of the terms = 48 = 4 a ⇒ a = 12 Given, 12 - 3 d 12 + 3 d 12 - d 12 + d = 27 35 ⇒ 9 4 - d 4 + d 12 - d 12 + d = 27 35 ⇒ 16 - d 2 35 = 144 - d 2 3 ⇒ 35 d 2 - 3 d 2 = 16 × 35 - 144 × 3 ⇒ 32 d 2 = 16 35 - 27 = 16 × 8 ⇒ d 2 = 4 ⇒ d = ± 2 So the numbers are: 6,10,14,18