Example 2.1.1.

Can you find the next term in the following sequences?

1. \(\displaystyle 7,7,7,7,7, \ldots\)

2. \(\displaystyle 3, -3, 3, -3, 3, \ldots\)

3. \(\displaystyle 1, 5, 2, 10, 3, 15, \ldots\)

4. \(\displaystyle 1, 2, 4, 8, 16, 32, \ldots\)

5. \(\displaystyle 1, 4, 9, 16, 25, 36, \ldots\)

6. \(\displaystyle 1, 2, 3, 5, 8, 13, 21, \ldots\)

7. \(\displaystyle 1, 3, 6, 10, 15, 21, \ldots\)

8. \(\displaystyle 2, 3, 5, 7, 11, 13, \ldots\)

9. \(\displaystyle 3, 2, 1, 0, -1, \ldots\)

10. \(\displaystyle 1, 1, 2, 6, \ldots\)