Calculation of the last term in the series
The given series is x², x, 1, ... (up to 31 terms).

Finding the pattern
To find the pattern in the series, we can observe that each term is one less than the square of the previous term. For example, the first term x² is one less than the square of x, and the second term x is one less than 1 squared.

Applying the pattern
We can continue this pattern to find the next terms in the series.
- The 4th term is 0 (1 less than 1 squared).
- The 5th term is -1 (1 less than 0 squared).
- The 6th term is -2 (1 less than -1 squared).
- And so on...

Finding the last term
To find the last term in the series, we need to continue this pattern up to the 31st term.
- Continuing the pattern, we find that the 31st term is -30 (1 less than -29 squared).
Therefore, the last term of the series x², x, 1, ... up to 31 terms is -30.