Number series – rule of “double then add an increasing integer”: 6, 13, 28, 59, ? Determine the next term when each step doubles and then adds 1, 2, 3, … sequentially.

Introduction / Context:A frequent construction in series questions is “multiply, then add a steadily increasing small integer.” It feels multiplicative but also embeds a linear count, making it both memorable and testable.

Given Data / Assumptions:

• Sequence: 6, 13, 28, 59, ?
• Hypothesis: next = 2*previous + k, with k rising by 1 each step.

Concept / Approach:Check if 13 = 2*6 + 1; if yes, try 28 = 2*13 + 2; continue to validate. If consistent, extend to find the next term using k = 4.

Step-by-Step Solution:

Verification / Alternative check:Back-substituting confirms all steps align with +1, +2, +3; therefore +4 is the natural continuation.

Why Other Options Are Wrong:

Common Pitfalls:Mistaking this for pure doubling or a quadratic; the small additive ladder is the key.

Final Answer:122