I can't seem to figure out the pattern in this:
1001, 502, 254, 110, __, __
neither could I, this was definitely not one to "guess" at ... I got a cubic regression to fit the data using my calculator.
$\displaystyle y = -24.5x^3 + 272.5x^2 - 1145x + 1898$
$\displaystyle y(1) = 1001$
$\displaystyle y(2) = 502$
$\displaystyle y(3) = 254$
$\displaystyle y(4) = 110$
$\displaystyle y(5) = -77$
$\displaystyle y(6) = -454$
whoever came up with this should be slapped.