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Odd and even numbers - class-VI
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If the number of consecutive odd integers whose sum can be expressed as $50^2 - 13^2$ is k then k, can be
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A
37
💡 Explanation:
Sum of odd $n$ consecutive numbers $n^2$
$\therefore (1+3+5\dots\dots (2n-1))=n^2$
where $n$ represents the number of terms.
$\therefore 50^2=1+3+5\dots 99=50\text{ }terms$
$\therefore 13^2=1+3+5\dots 25=13\text{ }terms$
$\therefore 50^2-13^2$$=(1+3+5\dots 99)-(1+3+5\dots 25)\=(27+29\dots 99)\ =37\text{ }terms.$