Let a 1 , a 2 , a 3 , … . be a G.P. of increasing positive numbers. Let the sum of its 6 th and 8 th terms be 2 and the product of its 3 rd and 5 th terms be 1 9 . Then 6 a 2 + a 4 a 4 + a 6 is equal to

Step-by-step solution

Given, a 1 , a 2 , a 3 , … . be a G.P. of increasing positive numbers, And the sum of its 6 th  and 8 th  terms be 2 So, a 6 + a 8 = 2 ⇒ a r 5 + a r 7 = 2     . . . . . 1 And the product of its 3 rd  and 5 th  terms be 1 9 , So, a 3 · a 5 = 1 9 ⇒ a 2 · r 2 · r 4 = 1 9 ⇒ a r 3 = 1 3 Now from putting the value of a r 3 = 1 3 in equation 1 we get, r 2 3 + r 4 3 = 2 ⇒ r 4 + r 2 = 6 ⇒ r 2 + 3 r 2 - 2 = 0 ⇒ r 2 = 2 a r 3 = 1 3 ⇒