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'Consecutive Negative Numbers' printed from http://nrich.maths.org/
Do you notice anything about the solutions when you add and/or
subtract consecutive negative numbers?
Take, for example, four consecutive negative numbers, say $$^-7,
^-6, ^-5, ^-4$$ Now place $+$ and/or $-$ signs between them.
e.g. $$^-7 + ^-6 + ^-5 + ^-4$$ $$^-7 - ^-6 + ^-5 - ^-4$$
There are other possibilities. Try to list all of them.
Now work out the solutions to the various calculations.
e.g. $$^-7 + ^-6 + ^-5 + ^-4 = ^-22$$ $$^-7 - ^-6 + ^-5 - ^-4 =
^-2$$ Choose a different set of four consecutive negative numbers
and repeat the process.
Take a look at both sets of solutions. Notice anything?
Can you explain any similarities?
Can you predict some of the solutions you will get when you start
with a different set of four consecutive negative numbers?
Test out any conjectures you may have.
Try to explain and justify your findings.