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.
