5040, 720, 120, 24, 4, 2
Series Analysis: Identifying the WRONG Number
The question requires finding the incorrect term in the number series: 5040, 720, 120, 24, 4, 2.
Investigating the Number Series Pattern
Let's examine the relationship between the numbers in the series. Observe the sequence:
- 5040
- 720
- 120
- 24
- 4
- 2
Consider the possibility of factorials:
- $7! = 7 \times 6 \times 5 \times 4 \times 3 \times 2 \times 1 = 5040$
- $6! = 6 \times 5 \times 4 \times 3 \times 2 \times 1 = 720$
- $5! = 5 \times 4 \times 3 \times 2 \times 1 = 120$
- $4! = 4 \times 3 \times 2 \times 1 = 24$
- $3! = 3 \times 2 \times 1 = 6$
- $2! = 2 \times 1 = 2$
The series closely follows the pattern of decreasing factorials starting from $7!$.
Comparing Given Series with Factorial Pattern
Let's align the given series with the expected factorial sequence:
| Position | Given Series | Expected Factorial Term | Matches? |
|---|---|---|---|
| 1 | 5040 | $7! = 5040$ | Yes |
| 2 | 720 | $6! = 720$ | Yes |
| 3 | 120 | $5! = 120$ | Yes |
| 4 | 24 | $4! = 24$ | Yes |
| 5 | 4 | $3! = 6$ | No |
| 6 | 2 | $2! = 2$ | Yes |
The table shows that the number '4' in the fifth position does not fit the factorial pattern. The expected number for this position is $3!$, which is 6.
Conclusion: WRONG Number Identification
Based on the analysis, the number 4 is the incorrect term in the series. It deviates from the established pattern of decreasing factorials ($7!, 6!, 5!, 4!, 3!, 2!$).
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