kth arithmetic mean between two numbers for JEE

Formula

\(A_k=a+kd=a+\frac{k(b-a)}{n+1}\)

Variables: \(a,b\): given numbers, \(n\): number of arithmetic means inserted, \(k=1,2,\dots,n\), \(A_k\): kth arithmetic mean.

Conditions: When \(a, A_1,\dots,A_n,b\) form an AP.

Finding specific inserted arithmetic means.