The sum of first n odd natural numbers

Question:

The sum of first n odd natural numbers is ___________.

Solution:

First n odd natural numbers are 1, 3, 5, 7, ............. n

Here first term a = 1

Common difference = 2

Sum of A.P is

$\frac{n}{2}\{2 a+(n-1) d\}$

$=\frac{n}{2}\{2(2)+(n-1) 2\}$

$=\frac{n}{2}\{4+2 n-2\}$

$=\frac{n}{2}\{2+2 n\}$

i.e Sum of first n even numbers = n(n + 1).

 

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