Prove that the sum of n arithmetic means between two numbers is n times the single A.M. between them.

Let a and b be two given numbers.
Let be A.M.'s between a and b.

∴    a, b are in A.P.

                                                 {∵   First term = a, last term = b and number of terms = n + 2}

                                
                                    = n times the single A.M. between a and b.