Write the sum of first n even natural numbers.

1.	Write the sum of first n even natural numbers.
Answer» First n even Natural numbers are 2, 4, 6,……, 2n This forms an A.P where a= 2 l= 2n where l is last term of the A.P S_n = \(\frac{n}{2}\)(2a + (n–1) d) or \(\frac{n}{2}\)(a + l) = \(\frac{n}{2}\)(2 + 2n) = \(\frac{n}{2}\)[2(1 + n)] = n (n + 1)

Answer»

First n even Natural numbers are 2, 4, 6,……, 2n

This forms an A.P where

a= 2

l= 2n

where l is last term of the A.P

S_n = \(\frac{n}{2}\)(2a + (n–1) d) or \(\frac{n}{2}\)(a + l)

= \(\frac{n}{2}\)(2 + 2n)

= \(\frac{n}{2}\)[2(1 + n)]

= n (n + 1)

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