Recursive construction – multiply by n and add n: 1, 2, 6, 21, 88, 445, ? — Find the next term.

Introduction / Context:Here each step multiplies by an increasing integer and then adds that same integer: ×1 +1, ×2 +2, ×3 +3, etc.

Observation / Approach:

• 1 × 1 + 1 = 2
• 2 × 2 + 2 = 6
• 6 × 3 + 3 = 21
• 21 × 4 + 4 = 88
• 88 × 5 + 5 = 445
• Next uses 6: 445 × 6 + 6 = 2676

Step-by-Step Solution:Compute 445 × 6 + 6 = 2670 + 6 = 2676.

Verification / Alternative check:The pattern of “×n then +n” is consistent from the first transition onward.

Why Other Options Are Wrong:Other values do not equal 445 × 6 + 6 and thus break the recursive rule.

Common Pitfalls:Using “×n + (n−1)” or a constant adder; both fail earlier steps.

Final Answer:2676