Q. 184.4( 7 Votes )
Find the sum of first n even natural numbers.
First n even natural numbers are 2, 4, 6,…, 2n.
To find: sum of these n even natural numbers.
The even natural numbers forms an AP with first term 2 and common difference 2.
Now, Sum of first n terms of an AP is given by:
Sn = [2a + (n - 1)d]
where a is the first term and d is the common difference.
∴ Sum of first n natural numbers is given by:
Sn = [2(2) + (n - 1)(2)]
= [4 + 2n - 2]
= [2n + 2]
= n (n + 1)
∴ Sum of first n even natural numbers is n(n + 1).
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The sum of n terms of an A.P. is 3n2+ 5n. Find the A.P. Hence, find its 16th term.KC Sinha - Mathematics