Question

The sum of first twenty even natural number is​

Answer 1

Answer:

The sum of the first twenty even natural numbers is 420.

Explanation:

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

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