Geometric means form a GP for JEE

Formula

\(a, G_1, G_2,\dots,G_n,b\text{ are in GP}\iff G_k=a\left(\frac{b}{a}\right)^{\!\frac{k}{n+1}}\)

Variables: \(a,b\): end terms, \(G_k\): inserted geometric means.

Conditions: \(k=1,2,\dots,n\); ratio defined in the real domain.

Recognizing and generating inserted geometric means.