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'Consecutive Negative Numbers' printed from https://nrich.maths.org/
Well done to Edison, from STC School in Hong
Kong, and to Esther, who both sent us correct solutions. Here is
Esther's solution:
The first thing I did was to list all the combinations of +
and - signs that were possible and then I tried them out on two
sets of consecutive negative numbers.
I noticed that the answers to some of them were the same so I
tried to work out the general formulae using consecutive numbers
$n$, $n+1$, $n+2$, $n+3$.
The results I got are in the table below:
| Operations |
-8, -7, -6, -5 |
-10, -9, -8, -7 |
Formula |
| + + + |
-26 |
-34 |
4n + 6 |
| + + - |
-16 |
-20 |
2n |
| + - + |
-14 |
-18 |
2n + 2 |
| + - - |
-4 |
-4 |
-4 |
| - + + |
-12 |
-16 |
2n + 4 |
| - + - |
-2 |
-2 |
-2 |
| - - + |
0 |
0 |
0 |
| - - - |
10 |
14 |
-2n - 6 |