No you cannot. You might guess that the next terms are:
\(\displaystyle 7\)
\(\displaystyle -3\)
\(\displaystyle 4\)
64
49
34
28
17
\(\displaystyle -2\)
\(\displaystyle 24\)
In fact, those are the next terms of the sequences I had in mind when I made up the example, but there is no way to be sure they are correct.
Still, we will often do this. Given the first few terms of a sequence, we can ask what the pattern in the sequence suggests the next terms are.