Average of first n even numbers

Even numbers are 2,4,6,8,10,….

Average = sum of elements/ no of elments

Now we will see the sum of elements:

Sum of first 2 even numbers: 2+4= 6= 2(2+1)

Sum of first 3 even numbers: 2+4+6= 12= 3(3+1)

Sum of first 4 even  numbers: 2+4+6+8=20= 4(4+1)

Sum of first 5 even numbers: 2+4+6+8+10 = 30 = 5(5+1)

Sum of first n even numbers: 2+4+6+8+10+. . . . .  n numbers= n(n+1)

Now we will see average:

Average of first 2 even numbers= (2+4)/2

                                                          = 6/2

                                                                =3

Average of first 3 even numbers= (2+4+6)/3

                                                          = 12/3

                                                                =4

Average of first 4 even numbers= (2+4+6+8)/4

                                                          = 20/4

                                                                =5

Average of first 5 even numbers= (2+4+6+8+10)/5

                                                          = 30/5

                                                                =6

Average of first n even numbers= (2+4+6+8+10+ . . .  . . n numbers)/n

                                                          = n(n+1)/n

                                                                =n+1

Since from above formula we can write directly as below:

Average of first 2  even numbers = n+1 = 2+1= 3

Average of first 3 even  numbers = n+1 = 3+1=4

Average of first 4 even  numbers = n+1 = 4+1=5

Average of first 5 even numbers = n+1 = 5+1=6