average of first n natural numbers

The natural numbers are 1,2,3,4,5,. . . . . .

now we will see the sum of natural numbers

sum of first 3 natural numbers= 1+2+3=6

the above can be written as

sum of first 3 natural numbers= 1+2+3=6=3(3+1)/2

sum of first 4 natural numbers= 1+2+3+4=4(4+1)/2

then sum of n natural numbers=1+2+3+......n terms=n(n+1)/2

then the average formula = sum of elements/no of elements

the average of n natural numbers= sum of elements/ no of elements

=(n(n+1)/2)/n

=n(n+1)/2xn

=(n+1)/2

THE AVERAGE OF FIRST N NATURAL NUMBERS=(n+1)/2

The average of first 5 natural numbers

sum of 5 natural numbers=1+2+3+4+5=15

no of elements = 5

average = 15/5 =3

by formula = average of first 5 natural numbers = (n+1)/2 =(5+1)/2

=6/2

Arithmetic1