In an increasing geometric progression, the sum of the first and the last term is 99 , the product of the second and the last but one term is 288 and the sum of all the terms is 189 . Then, the number of terms in the progression is equal to

Step-by-step solution

G.P. is increasing, i.e. r > 1 . Given, a + a r n - 1 = 99 ,   a r ⋅ a r n - 2 = 288 and a 1 - r n 1 - r = 189 . a 1 + r n - 1 = 99 and a 2 r n - 1 = 288 ⇒ a 1 + 288 a 2 = 9 9 ⇒ a 2 + 288 = 99 a ⇒ a 2 - 99 a + 288 = 0 ⇒ a = 3,   96 ⇒ r n - 1 = 288 a 2 = 32 ,   1 32 As r > 1 ⇒ r n - 1 = 32   for   a = 3 Now, a 1 - r n 1 - r = 189 ⇒ 3 1 - r ⋅ r n - 1 1 - r = 189 ⇒ 1 - r ⋅ 32 1 - r = 63 ⇒ 1 - 32 r = 63 - 63 r &#865