What is the missing number in the following sequence?
2, 12, 60, 240, 720, 1440, _________, 0
Sequence Pattern Identification
To find the missing number, we need to identify the pattern in the sequence: 2, 12, 60, 240, 720, 1440, _________, 0.
Let's examine the relationship between consecutive terms:
- Term 2 / Term 1 = 12 / 2 = 6
- Term 3 / Term 2 = 60 / 12 = 5
- Term 4 / Term 3 = 240 / 60 = 4
- Term 5 / Term 4 = 720 / 240 = 3
- Term 6 / Term 5 = 1440 / 720 = 2
The pattern shows that each term is obtained by multiplying the previous term by a successively smaller integer, starting with 6.
Calculating the Missing Term
Following the pattern, the multiplier decreases by 1 for each subsequent term. Therefore, the multiplier to get the 7th term from the 6th term is 1.
- Missing Term = Term 6 × 1
- Missing Term = 1440 × 1
- Missing Term = 1440
Verifying the Sequence End
The next multiplier in the sequence would be 0.
- Next Term = Missing Term × 0
- Next Term = 1440 × 0
- Next Term = 0
This matches the final term of the sequence, confirming our identified pattern.
Conclusion
The missing number in the sequence is 1440.
Important Questions from Number Series
Select the number from among the given options that can replace the question mark (?) in the following series.
37, 52, 74, 104, 143, ?
Select the number that can replace the question mark (?) in the following series.
17, 19, 22, 27, 34, 45, 58,?Select the number from among the given options that can replace the question mark (?) in the following series.
10, 14, 31, 35, 73, 77, ?
Select the number from among the given options that can replace the question mark (?) in the following series.
215, 231, 256, 292, ?
Select the number from among the given options that can replace the question mark (?) in the following series.
6, 6, 8, 24, 28, 140, ?
