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average of first 100 odd numbers

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 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

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