Question

The sum of all first odd n natural number is

Answer 1

the sequence is 1,3,5,7.....(2n-1)
First term a= 1
common difference d = 2
Sn=
$\frac{n}{2} (2a + (n - 1)d) \\ \frac{n}{2} (2 \times 1 + (n - 1)2) \\ \frac{n}{2} (2 + 2n - 2) \\ \frac{n}{2} \times 2n \\ n \times n \\ {n}^{2}$
hope this helps you:)))
don't forget to do it brainleist.

Answer 2

Hello,

This is a problem of Arithmetic Progression
The A.P. is 1,3,5,7
Here t = 1
and d = 3 - 1 = 2
n = n
The formula to find the sum of all numbers is
Sn = n/2(2t + (n - 1)d)
$= \frac{n}{2}(2 + (n - 1)2) \\ = \frac{n}{2} (2 + 2n - 2) \\ = \frac{n}{2} (2n) \\ = \frac{2 {n}^{2} }{2}$
= n^2
Hope this helps you :-)