Number series – constant second difference (increase first differences by 24): 13, 25, 61, 121, 205, ?

Introduction / Context:
If first differences form an arithmetic progression, the original series is quadratic-like. Extending the first-difference AP gives the next term smoothly.

Given Data / Assumptions:

• First differences: 25−13=12, 61−25=36, 121−61=60, 205−121=84.

Concept / Approach:
Differences grow by +24 each time: 12, 36, 60, 84 → next is 108. Add 108 to the last term.

Step-by-Step Solution:

Verification / Alternative check:
Reverse-check: 313−205=108 maintains the +24 ladder.

Why Other Options Are Wrong:

Common Pitfalls:
Mistaking this for a multiplicative series; the additive structure fits perfectly.

Final Answer:
313