Let A 1 , A 2 , A 3 , … … be an increasing geometric progression of positive real numbers. If A 1 A 3 A 5 A 7 = 1 1296 and A 2 + A 4 = 7 36 , then, the value of A 6 + A 8 + A 10 is equal to

Step-by-step solution

Given A 1 A 3 A 5 A 7 = 1 1296 Expanding using A n = A 1 r n - 1 formula we get, ⇒ A 1 A 1 r 2 A 1 r 4 A 1 r 6 = 1 1296 ⇒ A 1 4 r 12 = 1 1296 ⇒ A 1 r 3 = 1 6           . . . i Also given , A 2 + A 4 = 7 36 ⇒ A 1 r + A 1 r 3 = 7 36 ⇒ A 1 r + 1 6 = 7 36 ⇒ A 1 r = 1 36       . . . ii Dividing equation (i) from equation (ii) we get, r 2 = 6 Now A 6 + A 8 + A 10 = A 1 r 5 + A 1 r 7 + A 1 r 9 = A 1 r 3 r 2 + r 4 + r 6 = 1 6 6 + 36 + 216 = 43