You can never see a question like this on the GMAT, for two reasons. First, the GMAT never tests whether you understand how to sum an infinite series. Second, they can never give you the first few terms of a sequence and ask you to guess what the next terms will be; they need to tell you some rule that allows you to logically work out what the later terms are. Otherwise it's just a matter of guessing what the question designer was thinking, and the GMAT does not test whether you are psychic. If you know the first few terms of a sequence, there are always many perfectly logical ways to continue the sequence. For example, if I provide the sequence:
4, 4, 2, 2, ...
what is the next term? It would be logical to think the next term was 0, of course, but it would also be logical to think the next term was 3 (the sequence might be giving the number of primes between 0 and 10, between 10 and 20, between 20 and 30, between 30 and 40, and so on). There are certainly other possibilities (perhaps a_n = 0.5*(a_(n-2)), and the next term is 1, for example). There is no correct answer. The same is true given the first few terms of any sequence, though it's more difficult to provide simple examples when the numbers are complicated, as in the question above.
In any case, the question above could never appear on the GMAT.
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