What should come in place of question mark '?' in the following number…

Concept: In a position-based number series, each term is generated by a rule of the form f(n) = nn − c: raise the term's position n to its own power and adjust by a constant c. To find such a rule, test whether it fits every given term for n = 1, 2, 3, … before applying it to the missing term.

Application: Verify the rule against every known term, then extend it to the missing one.

1. Label the four given terms with positions n = 1, 2, 3, 4: −1, 2, 25, 254.

2. 11 − 2 = 1 − 2 = −1, which matches the first term.

3. 22 − 2 = 4 − 2 = 2, which matches the second term.

4. 33 − 2 = 27 − 2 = 25, which matches the third term.

5. 44 − 2 = 256 − 2 = 254, which matches the fourth term, confirming the rule nn − 2 holds across the whole series.

6. Apply the same rule to the missing fifth term, n = 5: 55 − 2 = 3125 − 2 = 3123.

Cross-check: Verify 55 independently by direct multiplication: 5 × 5 × 5 × 5 × 5 = 3125. Subtracting 2 gives 3123, the same value obtained from the rule, confirming the missing term.