Express $15^{3}$ as the sum of consecutive odd numbers.

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Solution

Let the three numbers be $(x - 1), x$ and $(x + 1)$ .

Given, the sum of three consecutive odd numbers is $15^{3}$ .
$\Rightarrow 15^{3} = 3375$ .

$∴ (x - 1) + x + (x + 1) = 3375$
$\Rightarrow$ $3 x = 3375$
$\Rightarrow$ $x = 1125$ .

Therefore,
$1^{s t}$ number $= x - 1 = 1125 - 1 = 1124$ .
$2^{n d}$ number $= x = 1125$ .
$3^{r d}$ number $= x + 1 = 1125 + 1 = 1126$ .

Hence, the three consecutive numbers are $1124, 1125, 1126$ .

Then, $1124 + 1125 + 1126 = 15^{3}$ .

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