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I am writing GRE in 2 two months, and I just can't solve these sequence question. Can anyone tell what the missing terms are and what is the pattern here?

Find the next 4 terms in this sneaky sequence:
1, 5, 4, 3, 7, 1, 10, -1, 13, -3, X1,X2,X3

I am supposed to guess the next three terms in the sequence (X1,X2,X3).

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42, 42, 42 (or 42, 42, 42, 42 if one wants 4 next terms). – Did Apr 4 '13 at 8:04
@Did I did not get the joke. – Dude Apr 4 '13 at 8:28
@Joe: See here. – Brian M. Scott Apr 4 '13 at 8:31
Any other Pomona alumni (or any Pomona alumnae) who want to join me in holding out for $47,47,47$ instead of Did’s $42,42,42$? – Brian M. Scott Apr 4 '13 at 8:32
@BrianM.Scott yup this is what I suspected first :) – Dude Apr 4 '13 at 8:36
up vote 4 down vote accepted

Try looking at the sequence this way:

1     4     7    10    13
   5     3     1    -1    -3

The top part of the sequence increases by 3 each time and the bottom part of the sequence decreases by 2 each time. The next 3 terms are therefore 16, -5 and 19.

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If there are no further restrictions on the sequence, any choice of $X_1,X_2,X_3$ is equally valid. It is always possible to construct a polynomial of degree $n$ that passes through $n+1$ datapoints.

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+1 I know. Why do they always ask these dumb questions on the GRE (or any standardized test). Is this something recent? Because a few years ago when I took the GRE (both general and math subject) I don't remember stupid questions like this. – Fixed Point Apr 4 '13 at 9:00

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