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The first 5 outputs are:
As you can see, the outputs keep doubling each time we increment x by 1.
This can be written formally, observing that if you know the value of , the next value will be
So, again, we've shown that the next value is twice the previous one, so you have
F(x) = (x + 1)(x - 2)
f(x) = x(x - 2) + 1(x - 2)
f(x) = x(x) - x(2) + 1(x) - 1(2)
f(x) = x² - 2x + x - 2
f(x) = x² - x - 2
f(x) = x(x - 2) + 1(x - 2)
f(x) = x(x) - x(2) + 1(x) - 1(2)
f(x) = x² - 2x + x - 2
f(x) = x² - x - 2