The product of three consecutive terms of a G . P . is 512 . If 4 is added to each of the first and the second of these terms, the three terms now form an A . P . , then the sum of the original three terms of the given G . P . is :

Step-by-step solution

To minimize the calculation, 3 numbers in G . P . can be taken as a r ,   a ,   a r where, a is the first term and r is the common ratio. Given product of three numbers is 512 . ⇒ a r . a . a r = 512 ⇒ a 3 = 8 3 ⇒ a = 8 Also given, a r + 4 ,   a + 4 ,   a r are in A . P . ⇒ 2 a + 4 = a r + 4 + a r Putting a = 8 , we get 2 12 = 8 r + 4 + 8 r ⇒ 2 r 2 - 5 r + 2 = 0 ⇒ 2 r - 1 r - 2 = 0 ⇒ r = 2 or 1 2 Hence, numbers may be 4 ,   8 ,   16 or 16