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 \(= n^2\).

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3. Sum of first 'n' odd natural numbers