Extend the series: 3, 8, 13, 24, 41, ? — detect the evolving jump sizes and project the next logical increment.

Introduction / Context:This rising sequence uses non-uniform differences that themselves grow in a recognizable way. Such constructions often increase by “larger and larger” steps that nonetheless follow a secondary trend you can extend.

Given Data / Assumptions:

• Sequence: 3, 8, 13, 24, 41, ?
• We focus on first differences to see the step pattern.

Concept / Approach:List the differences and analyze how they evolve. Here the step sizes accelerate in a controlled manner that can be continued to predict the next term reliably.

Step-by-Step Solution:

Verification / Alternative check:Projecting the “difference increments” shows a repeating growth behavior (rising by 6, then again by 6), so picking +29 as the next jump produces a smooth acceleration consistent with prior jumps.

Why Other Options Are Wrong:

• 75, 80, 85 would require next jumps of 34, 39, or 44, which exceed the inferred step evolution and break the observed growth rhythm.

Common Pitfalls:Forcing a constant-difference or ratio rule when the series is built from an evolving difference pattern. Always check how the differences themselves change.

Final Answer:70