Question

The sum of first n even natural numbers is:

(A) n square + n

(B) sigma 2n square

(C) n square

(D) n( n+1)/2

Answer 1

The answer is option (D).

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Answer 2

2, 4, 6,……..n

sum of AP = n/2 {2a + (n-1)d}

=n/2 {2*2 + (n-1)*2}

=n/2 {4 + 2n - 2}

=n/2 (2n+2)

=n(n+1)

= n^2 + n

(or)

The even natural numbers are

2, 4, 6, 8, ........

This is an A.P. with a = 2 & d = 2.

To find : Sn

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 + n