The sum of first $n$ consecutive odd numbers is equal to $n^{2}$ .

True

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False

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Solution

The correct option is A True
Factual

E.g. $1 + 3 = 2^{2} = 4$

$1 + 3 + 5 = 3^{2} = 9$

$1 + 3 + 5 + 7 = 4^{2} = 16$

$1 + 3 + 5 + 7 + 9 = 5^{2} = 25$

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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 $n^{2}$ .

n

n^{2}

n

n^{2}

n

n^{2} = \frac{n^{2} - 1}{2} + \frac{n^{2} + 1}{2}

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