Arithmetic means form an AP for JEE

Formula

\(a, A_1, A_2,\dots,A_n,b\text{ are in AP}\iff A_k=a+\frac{k(b-a)}{n+1}\)

Variables: \(a,b\): end terms, \(A_k\): inserted arithmetic means.

Conditions: \(k=1,2,\dots,n\).

Recognizing and generating inserted arithmetic means.