8. Find the sum of the first n even natural numbers. Hence find the sum of first 20 even natural numbers.
Sol. The first n even natural numbers are as follows
2, 4, 6, 8, ...........
These numbers form an A.P. with a = 2, d = 2
Sn = n/2[2a + (n – 1)d]
∴ Sn = n/2[2 (2) + (n – 1) 2]
∴ Sn = n/2[4 + 2n – 2]
∴ Sn = n/2[2n + 2]
∴ Sn = n/2 × 2 (n + 1)
∴ Sn = n (n + 1)
∴ S20 = 20 (20 + 1)
∴ S20 = 20 (21)
∴ S20 = 420
∴ Sum of first twenty even natural numbers is 420.