If in a G.P. of 64 terms, the sum of all the terms is 7 times the sum of the odd terms of the G.P, then the common ratio of the G.P. is equal to

Step-by-step solution

For the given GP, n = 64 , S n = 7 S o ; where S o → Sum of odd terms ⇒ a + ar + ar 2 + ar 3 + . . . + ar 63 = 7 a + ar 2 + ar 4 … . . + ar 62 ⇒ a 1 - r 64 1 - r = 7 a 1 - r 64 1 - r 2 ⇒ 1 - r 64 = 7 1 - r 64 1 + r ⇒ 1 = 7 1 + r ⇒ 1 + r = 7 ⇒ r = 6