If the numbers 3 2 a - 1 , 14, 3 4 - 2 a 0 < a < 1 are the first three terms of an arithmetic progression, then its fifth term is equal to

Step-by-step solution

Given, 3 2 a - 1 + 3 4 - 2 a = 28 ⇒ 9 a 3 + 81 9 a = 28 Put 9 a = x ⇒ x 3 + 81 x = 28 x 2 + 243 = 84 x ⇒ x 2 - 84 x + 243 = 0 ⇒ x = 81 or 3 ⇒ 9 a = 81 or 3 ⇒ a = 2 or 1 2 Since, a∈ 0 , 1 ⇒ a = 1 2 So, the numbers are 1 , 14 , 27 which are in A.P. with d = 13 Hence, t 5 = a + 4 d = 1 + 4 × 13 = 53