Question

Find six geometrical mean between 27 and 1/81

Answer 1

Let the required GM is g1, g2, g3, g4, g5, g6

= 27, g1, g2, g3, g4, g5, g6, are in GP

Now a = 27 and = 8th element

⇒ 1/81 = ar7 ⇒ 1/81 = 27.r7

⇒ 1/(81 x 27) = r7

⇒ r7 = 1/37

⇒ r = 1/3

∴ the six GM are 9, 3, 1, 1/3, 1/9, 1/27