0, 6, 24, 60, ______
Number Series Pattern Recognition
The question asks to identify the next number in the sequence: 0, 6, 24, 60, ______. We need to find the underlying mathematical pattern.
Identifying the Series Pattern
Let's examine the relationship between the position of the term (n) and the term value. We can test a pattern involving cubes:
- For n=1: $1^3 - 1 = 1 - 1 = 0$
- For n=2: $2^3 - 2 = 8 - 2 = 6$
- For n=3: $3^3 - 3 = 27 - 3 = 24$
- For n=4: $4^3 - 4 = 64 - 4 = 60$
The pattern holds true. Each term is generated by the formula $T_n = n^3 - n$.
Calculating the Next Term
To find the next number in the series, we need to calculate the 5th term (n=5) using the identified pattern:
For n=5: $T_5 = 5^3 - 5$
Calculation:
- $5^3 = 125$
- $T_5 = 125 - 5 = 120$
Conclusion
Therefore, the next number in the series is 120.
Similar Questions
- What should come in place of the question mark (?) in the given series?
3, −2, −12, −32, −72, ? - What should come in place of the question mark (?) in the given series?
512 513 505 532 468 ? - Identify the number that does NOT belong to the following series.
14, 19, 26, 35, 44, 59 - Select the number from among the given options that can replace the question mark (?) in the following series.
16, 25, 36, 49, ? Select the number from among the given options that can replace the question mark (?) in the following series.
5, 18, 39, 68, 105, ?
- Select the number that can replace the question mark (?) in the following series.
14, 2, 28, 3, 84, 4, ? - Select the number from among the given options that can replace the question mark (?) in the following series.
40, 36, 33, 31, ? - Select the number from among the given options that can replace the question mark (?) in the following series.
256, 625, 1296, 2401, ? - Select the number from among the given options that can replace the question mark (?) in the following series.
4, 6, 8, 18, 16, ? - Select the number set from among the given options that can replace the question mark (?) in the following series.
4 : 9, 25 : 49, ?, 289 : 361
Important Questions from Number Series
What will come in place of question mark (?) in the following number series?
2, 5, 11, 23, 44, 77, ?
What will come in place of question mark (?) in the following number series?
31, 32, 36, ?, 61, 86
What will come in the place of question mark (?) in the following number series?
3, 6, 18, ?, 630, 6930
What should come in place of the question mark ‘?’ in the following number series?
60, 40, 50, ?, 180, 460
A series is given with one term wrong. Select that wrong term from the given alternatives.
J12, M24, P48, S96, U192
