The sum of infinitely many terms of a geometric progression is 3 times the sum of even terms. If the first term is non-zero, then the common ratio of the geometric progression is

Step-by-step solution

S 1 = a + a r + a r 2 + . … … + a r n - 1 + . … … . ∞ S 2 = a r + a r 3 + a r 5 + . … … ∞ S 1 = a 1 - r , S 2 = a r 1 - r 2 Given S 1 = 3 S 2 ⇒ a 1 - r = 3 a r 1 - r 2 ⇒ 1 = 3 r 1 + r ⇒ 1 + r = 3 r ⇒ r = 1 2