Write the sum of first n odd natural numbers.

Question:

Write the sum of first n odd natural numbers.

Solution:

We need to find the sum of 1, 3, 5, 7... upto n terms.

Here, a = 1, d = 2

We know:

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

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

$=n^{2}$

Therefore, the sum of the first $n$ odd numbers is $n^{2}$.

 

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