Sum of the first $n$ odd natural numbers is

2 n + 1

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n^{2}

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n^{2} - 1

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2 n^{2} + 1

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Solution

The correct option is B $n^{2}$
Consider the odd natural numbers.

$1, 3, 5, 7, . . . . . . . . . ., (2 n - 1)$

We know that the sum of $n$ numbers

$= \frac{n}{2} [2 a + (n - 1) d]$

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

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

$= n^{2}$

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Similar questions

$1 + 3 + 5 + . . . . . + (2 n - 1) = n^{2}$ i.e., the sum of first n odd natural numbers is $n^{2}$ .

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Question 12

Write the correct answer from the given four options.

The sum of first n odd natural numbers is

a) $2 n + 1$
b) $n^{2}$
c) $n^{2} - 1$
d) $n^{2} + 1$

1.3.5 . . . . . (2 n - 1) > n^{n}, n ϵ N

n

n^{2}

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