I was reading a math book in a bookstore a few months ago, and it explained that the typical question on a standardized test, whereby you have to say which number comes next in a sequence, is actually illegitimate. The reason is that you can always find more than one formula to generate the next number, where the different formulas give the same initial numbers (matching the ones in the question). For example:
Choose the number that comes next: 2, 4, 6, ___
(d) none of the above
You're thinking the answer is (a), right? And yes, the formula f(n)=2n would certainly match the first three numbers in the question, and would also make 8 the next number.
But the formula f(n)=2n + (n-1)(n-2)(n-3) also works; the right term is zero for the first three iterations, so it gives the same results as the simpler formula, but after that it gives different results. And if you plug n=4 into this formula, the next number in the sequence is 14, so answer (c) is perfectly reasonable. Indeed, (I think) you could come up with a formula for any desired fourth number in the sequence, by appropriately multiplying the right term by some constant.
So not only are the SATs and GREs racist and sexist, they also discriminate against wise aleck math geniuses! (This is not to suggest that blacks and women can't be math geniuses.)
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