Write the sum of first n odd natural numbers.

1.	Write the sum of first n odd natural numbers.
Answer» First n odd numbers are 1, 3, 5, 7, 9........., (2n–1) which forms an A.P a= 1 l= 2n – 1 where l be the last term S_n = \(\frac{n}{2}\)(2a + (n–1) d) or \(\frac{n}{2}\)(a + l) = \(\frac{n}{2}\)(1 + 2n –1) = \(\frac{n}{2}\)(2n) =n (n) =n²

Answer»

First n odd numbers are 1, 3, 5, 7, 9........., (2n–1) which forms an A.P a= 1

l= 2n – 1 where l be the last term

S_n = \(\frac{n}{2}\)(2a + (n–1) d) or \(\frac{n}{2}\)(a + l)

= \(\frac{n}{2}\)(1 + 2n –1)

= \(\frac{n}{2}\)(2n)

=n (n)

=n²

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