If G1 and G2 are 2 geometric means between a and b show that: (a) G1G2 = ab (b) (G1^2/ G2) + ( G2^2/G1) = a + b.

let a be the first term so it is equal to a. G1 is ar . G2 is ar²  . b is ar3
a) multiply G1 and G2 we will get a²r³. on multiplying a and b the same result is obtained. hence proved.

b) G1^2/G2 = a²r²/ar² = a          G2^2/G1 = a²r⁴/ar = ar³ = b
                     on adding this both we obtain a + b hence proved