Solution 2.1.1.1.

No you cannot. You might guess that the next terms are:

1. \(\displaystyle 7\)

2. \(\displaystyle -3\)

3. \(\displaystyle 4\)

4. 64

5. 49

6. 34

7. 28

8. 17

9. \(\displaystyle -2\)

10. \(\displaystyle 24\)

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.