Sum of first 'n' odd natural numbers — lesson. Mathematics State Board, Class 10.

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The odd natural numbers are

$1$ ,

$3$ ,

$5$ , ….

We need to find the value of

$1 + 3 + 5 + … + (2n - 1)$ .

First term,

$a = 1$ .

Common difference,

$d = 3 - 1 = 2$ .

Last term,

$l = 2n - 1$ .

This series is an

$A.P$ .

If the first term

$a$ , and the last term

$l$ are given, then

$S_{n} = \frac{n}{2} [a + l]$ .

Now, substitute the given values in

$S_n$ .

$S_{n} = \frac{n}{2} [1 + 2 n - 1]$

$S_{n} = \frac{n}{2} \times 2 n$

$S_n = n^2$

Therefore,

$S_n = n^2$ .

Sum of first

$n$ odd natural numbers

$= n^2$ .

Did you find an error?

3. Sum of first 'n' odd natural numbers