The sum of first four terms of a geometric progression G . P . is 65 12 and the sum of their respective reciprocals is 65 18 . If the product of first three terms of the G . P . is 1 , and the third term is α , then 2 α is _________.

Step-by-step solution

Let number are a , a r , a r 2 , a r 3 a r 4 - 1 r - 1 = 65 12   … 1 1 a 1 r 4 - 1 1 r - 1 = 65 18 1 a r 3 1 - r 4 1 - r = 65 18   … 2 1 2 ⇒ a 2 r 3 = 3 2 and a 3 · r 3 = 1 a r = 1 a r 2 · r = 3 2 r = 3 2 , a = 2 3 So, third term = a r 2 = 2 3 × 9 4 α = 3 2 2 α = 3