Find the sum of the first n even natural numbers. Hence find the sum of first 20 even natural numbers.

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.