The first, second and seventh terms of an arithmetic progression (all the terms are distinct) are in geometric progression and the sum of these three terms is 93 . Then, the fourth term of this geometric progression is

Step-by-step solution

Let a , a + d , a + 6 d are in G.P. ⇒ a + d 2 = a a + 6 d ⇒ a 2 + d 2 + 2 a d = a 2 + 6 a d ⇒ d 2 = 4 a d ⇒ d = 4 a Also, given that the sum of the terms is 93 . ⇒ a + a + d + a + 6 d = 93 3 a + 7 d = 93 3 a + 7 4 a = 93 31 a = 93 ⇒ a = 3 & d = 12 ⇒ the terms are 3 , 15 , 75 ⇒ the fourth term of the GP.. is 75 × 5 = 375