Alternate operations series (+3 then ×2) Complete the pattern: 5, 10, 13, 26, 29, 58, 61, ( ... ).

Introduction / Context:
Many numeric series alternate between two simple operations. Detecting the alternation and applying it to the last term yields the next value quickly. This question mixes addition and multiplication in a predictable cycle.

Given Data / Assumptions:

• Series: 5, 10, 13, 26, 29, 58, 61, ...
• We expect a repeating two-step operation.

Concept / Approach:
Check adjacent jumps: 5→10 (+5), 10→13 (+3), 13→26 (×2), 26→29 (+3), 29→58 (×2), 58→61 (+3). After +3 typically follows ×2. Therefore, apply ×2 to 61 to get the next term.

Step-by-Step Solution:
5 → 10: ×2.10 → 13: +3.13 → 26: ×2.26 → 29: +3.29 → 58: ×2.58 → 61: +3.61 → next: ×2 ⇒ 122.

Verification / Alternative check:
Write the pattern explicitly as (×2, +3) repeating. Starting from 5 gives the exact sequence given; so the next term must be 122.

Why Other Options Are Wrong:
125, 128, 64, 120 do not result from applying ×2 to 61 in this alternating pattern; they correspond to other operations not present here.

Common Pitfalls:
Assuming a constant difference or mixing the order (+3 then ×2 vs. ×2 then +3). Always trace from term to term to lock the alternation.

Final Answer:
122