Guess the terms in the sequence?

Question

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).

Answer 1

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.

Answer 2

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.