Q. 174.2( 9 Votes )
Find the sum of first n natural numbers.
First n natural numbers are 1, 2, 3,…, n.
To find: sum of these n natural numbers.
The natural numbers forms an AP with first term 1 and common difference 1.
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(1) + (n - 1)(1)]
= [2 + n - 1]
= [n + 1]
∴ Sum of first n natural numbers is n(n + 1)/2.
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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