Q27 of 97 Page 192

Find the value of n so that may be the geometric mean between a and b.

G.M of two numbers in G.P. is given by √ab

∴ = √ab

By squaring on both sides we get,

⇒ = ab

⇒

⇒ 2n+1 = 0

⇒ 2n = –1

⇒ n =

∴ Value of n for to be G.M is

If a, b, c and d are in G.P. show that (a² + b² + c²) (b² + c² + d²) = (ab + bc + cd)².

Insert two numbers between 3 and 81 so that the resulting sequence is G.P.

The sum of two numbers is 6 times their geometric mean, show that numbers are in the ratio .

If A and G be A.M. and G.M., respectively between two positive numbers, prove that the numbers are .