Number series with alternating operations: find the missing term to continue the pattern. Sequence given: 2, 3, 3, 5, 10, 13, ?, 43, 172, 177 Identify the rule and compute the value of the missing term. Choose the correct next number.

Pattern insight
The sequence alternates between “add an increasing odd number” and “multiply by an increasing integer”.

Detail
Start at 2: +1 → 3; ×1 → 3; +2 → 5; ×2 → 10; +3 → 13; ×3 → 39; +4 → 43; ×4 → 172; +5 → 177.

Result
The missing term after 13 is 13 × 3 = 39.

Common pitfall
Assuming a single arithmetic or geometric pattern; it is a mixed-operation pattern.