Find the next number in the given series: 2, 1; 24, 6, 720, 120, 40320, ?

Question

Find the next number in the given series:

2, 1; 24, 6, 720, 120, 40320, ?

1. A. 8160
2. B. 56740
3. C. 64280
4. D. 5040 (Correct answer)

Correct Answer

Option D — 5040

Detailed Solution & Explanation

The correct answer is 5040.

Key Points

• Every term is a factorial, taken in pairs of (higher, lower).
• 2 = 2!, 1 = 1!; then 24 = 4!, 6 = 3!; then 720 = 6!, 120 = 5!; then 40320 = 8!, so the missing term is 7!.
• 7! = 5040.

Additional Information

• Read as pairs, the pattern is (2!, 1!), (4!, 3!), (6!, 5!), (8!, 7!) — each pair takes an even factorial followed by the odd one just below it.
• Handy values: 5! = 120, 6! = 720, 7! = 5040, 8! = 40320.

*Ministry of Papers worked solution. The Commission has not yet published the official key for this paper; this answer will be reconciled with it on release.*