Number series (alternating *2 and +3): 5, 10, 13, 26, 29, 58, 61, (…) Find the next term by following the repeat pattern of operations.

Introduction / Context:Alternating-operation series are common: the same two steps repeat—typically a multiplication followed by an addition. Recognizing this cycle quickly yields the next term.

Given Data / Assumptions:

• Series: 5, 10, 13, 26, 29, 58, 61, (…)
• Observe pairing of operations between successive terms.

Concept / Approach:Identify a repeating pattern: ×2 then +3. Validate across all transitions, then apply to compute the next term.

Step-by-Step Solution:

Verification / Alternative check:Continue one more hypothetical step: 122 + 3 = 125 would be the following term, confirming the cycle consistency.

Why Other Options Are Wrong:

• 64, 125, 128: These correspond to misapplied steps (+3 at the wrong time or different multipliers).

Common Pitfalls:Applying +3 twice in a row or reversing the order. Always mark the positions of operations to avoid a mismatch.

Final Answer:122