Prove that the product `n` geometric means between two quantities is equal to the nth power of `a` geometric mean of those two quantities.

Explanation

Let a and b be the 2 numbers and G be the geometric mean between them.

Therefore a,b,G must be in G.P.

Common ratio ` =G/a​=b/G​`

`⇒G^2=ab`

`=>sqrt(G)=ab​...(1)`

Therefore,

a,G1​,G2​,......,Gn​,b form G.P.
with a as its first term and b as last and `(n+2)^(th)` term

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