Question 86 (iii)
The sum of first n natural numbers is given by 12n2+12n. Find
The sum of natural numbers from 11 to 30.
Given, sum of first n natural numbers =12n2+12n
Sum of natural numbers from 11 to 30.
= Sum of first 30 natural numbers - Sum of first 10 natural numbers
=[12(30)2+12(30)]−[12(10)2+12(10)]
=9002+302−1002−102 [divide each term by 2]
= 450 + 15 - 50 - 5 = 410