average of first 100 odd numbers

 Odd  numbers are 1,3,5,7,9,….

Average = sum of elements/  no  of elments

Now we will see the sum of elements:

Sum of first 2 odd  numbers: 1+3= 4= 22

Sum of first 3 odd  numbers: 1+3+5= 9= 32

Sum of first 4 odd  numbers: 1+3+5+7=16= 42

Sum of first 5 odd  numbers: 1+3+5+7+9 = 25 = 52

Sum of first n odd  numbers: 1+3+5+7+9+. . . . .  n numbers= n2

Now we will see average:

Average of first 2 odd numbers= (1+3)/2

                                                          = 4/2

                                                                =2

Average of first 3 odd  numbers= (1+3+5)/3

                                                          = 9/3

                                                                =3

Average of first 4 odd  numbers= (1+3+5+7)/4

                                                          = 16/4

                                                                =4

Average of first 5 odd numbers= (1+3+5+7+9)/5

                                                          = 25/5

                                                                =5

Average of first n odd  numbers= (1+3+5+7+9+ . . .  . . n numbers)/n

                                                          = nxn/n

                                                                =n
average of first 100 odd numbers=(1+3+5+7+9+ . . .  . . 100 numbers)/100

                                                          = 100x100/100

                                                                =100

Average of first n odd numbers = n                             

Since from above formula we can write directly as below:

Average of first 2  odd  numbers = n = 2

Average of first 3 odd  numbers = n = 3

                            Average of first 100 odd  numbers =n = 100