How can $13^{2}$ be written as the sum of two consecutive natural numbers? [3 marks]

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Solution

$To find the consecutive numbers, whose sum gives n^{2}, we have to find, \frac{n^{2} - 1}{2} and \frac{n^{2} + 1}{2} [1 m a r k] Hence we ca n write, \frac{13^{2} - 1}{2} and \frac{13^{2} + 1}{2} = 84 and 85 [2 m a r k s] 169 can be written as the sum of consecutive numbers 84 and 85 .$

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