Question #c044f

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Answer 1 · 2018-02-07T02:31:12

The numbers are 1, 3, 5 and 7. Proof of this follows...

To create a general expression for an odd number, we could write

$2 n + 1$ $2n+1$

because no matter what value $n$ $n$ might have, $2 n$ $2n$ is even, and $2 n + 1$ $2n+1$ is the next number, and must be odd.

So, our consecutive odd numbers would be:

$2 n + 1, 2 n + 3, 2 n + 5, 2 n + 7$ $2n+1, 2n+3, 2n+5, 2n+7$

Add them:

$2 n + 1 + 2 n + 3 + 2 n + 5 + 2 n + 7 = 16$ $2n+1+ 2n+3+ 2n+5+ 2n+7=16$

$8 n + 16 = 16$ $8n+16=16$

This is true only if $n = 0$ $n=0$

So, out number are 1, 3, 5 and 7