In an increasing geometric series, the sum of the second and the sixth term is 25 2 and the product of the third and fifth term is 25 . Then, the sum of 4 t h , 6 t h and 8 t h terms is equal to:

Step-by-step solution

a ,   a r ,   a r 2 .... T 2 + T 6 = 25 2 ⇒ ar 1 + r 4 = 25 2 a 2 r 2 1 + r 4 2 = 625 4       ⋯ 1 T 3 · T 5 = 25 ⇒ a r 2 a r 4 = 25 a 2 r 6 = 25       . . . 2 On dividing 1 by 2 1 + r 4 2 r 4 = 25 4 4 r 8 - 17 r 4 + 4 = 0 4 r 4 - 1 r 4 - 4 = 0 r 4 = 1 4 , 4 ⇒ r 4 = 4 (an increasing geometric series) a 2 r 6 = 25 ⇒ a r 3 2 = 25 T 4 + T 6 + T 8 = a r 3 + a r 5 + a r 7 = ar 3 1 + r 2 + r 4 = 5 1 + 2 + 4 = 35