Find the sum of the first n natural numbers and hence find the sum of first 20 natural numbers.

1. Find the sum of the first n natural numbers and hence find the sum of first 20 natural numbers.

Sol. The first n natural numbers are 1, 2, 3, 4, ............

These natural number form an A.P. with a = 1, d = 1

∴ Sn = n/2 [2a + (n – 1) d]

∴ Sn = n/2 [2 (1) + (n – 1) 1]

∴ Sn = n/2 [2 + n – 1]

∴ Sn = n/2 (n + 1)

∴ S20 = 20/2 (20 + 1)

∴ S20 = 10 (21)

∴ S20 = 210

∴ Sum of first twenty natural numbers is 210.