Number series – find the next term: 1, 5, 13, 25, 41, ? Observe the first differences (+4, +8, +12, +16). Continue the pattern to determine the missing term.

Introduction / Context:Many number-series items are built from regular first differences. When those first differences themselves rise by a fixed amount, the series is quadratic-like with constant second difference. Spotting that constant increment unlocks the answer quickly.

Given Data / Assumptions:

• Series: 1, 5, 13, 25, 41, ?
• We assume a clean deterministic rule continues.

Concept / Approach:Compute first differences and then check if those differences progress in a simple pattern (e.g., constant increment). If first differences increase by a constant k, then the next first difference is the previous one plus k.

Step-by-Step Solution:

Verification / Alternative check:If second difference is constant (+4), extending by +20 is consistent and yields a smoothly growing sequence without anomalies.

Why Other Options Are Wrong:

Common Pitfalls:Jumping to multiplicative rules or cubes prematurely. Always try first- and second-difference checks first.

Final Answer:61