The sum of an infinite geometric progression is 5 4 times the sum of all the odd terms. If the first term is non-zero, then the common ratio of the geometric progression is

Step-by-step solution

a , a r , a r 2 , a r 3 , a r 4 , a r 5 , … , ∞ S 1 = a + a r + a r 2 + a r 3 + … ∞ = a 1 - r S 2 = a + a r 2 + a r 4 + a r 6 + … + ∞ = a 1 - r 2 S 1 = 5 4 S 2 ⇒ a 1 - r = 5 4 a 1 - r 2 ⇒ a 1 - r = 5 4 a 1 - r 1 + r ⇒ 1 + r = 5 4 ⇒ r = 1 4