Question

Find the sum of first n odd natural numbers.

Answer 1

Here is the answer

First n natural numbers
1 , 3 , 5 , 7 , 9 ... ( 2n - 1 ).

$\bf{a = t_{1} = 1} \\ \bf{t_{n } =( 2n - 1)}$

$\bf{d = 2}$

Method 1 =>

$\bf{ s_{n} = \frac{n}{2} ( t_{1} + t_{n})}$

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

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

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

$\bf{ = {n}^{2} }$

Method 2

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

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

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

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

$\bf{ = {n}^{2} }$

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