Podcast
Questions and Answers
What is the first-order difference between the second and third terms of the sequence?
What is the first-order difference between the second and third terms of the sequence?
- 144
- 130
- 152 (correct)
- 96
What indicates that the sequence is following a quadratic pattern?
What indicates that the sequence is following a quadratic pattern?
- The second-order differences are constant. (correct)
- The first-order differences are increasing.
- The sequence has no specific pattern.
- The original sequence is linear.
What will be the next first-order difference after 488 in the sequence?
What will be the next first-order difference after 488 in the sequence?
- 192
- 288
- 240 (correct)
- 336
How much does the second-order difference change as we progress along the sequence?
How much does the second-order difference change as we progress along the sequence?
What is the predicted next term of the sequence using the identified pattern?
What is the predicted next term of the sequence using the identified pattern?
Flashcards
Quadratic Pattern
Quadratic Pattern
A pattern in a sequence where the second-order differences between consecutive terms are constant.
First-Order Differences
First-Order Differences
The differences between consecutive terms in a sequence.
Second-Order Differences
Second-Order Differences
The differences between consecutive first-order differences.
Polynomial Rule (Degree 2)
Polynomial Rule (Degree 2)
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Sequence Prediction
Sequence Prediction
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Constant Second-Order Differences
Constant Second-Order Differences
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1238
1238
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Study Notes
Number Pattern Analysis
- The given sequence is: 6, 62, 214, 510, 998, ?
- The differences between consecutive terms are:
- 62 - 6 = 56
- 214 - 62 = 152
- 510 - 214 = 296
- 998 - 510 = 488
- The differences between these differences are:
- 152 - 56 = 96
- 296 - 152 = 144
- 488 - 296 = 192
- The differences between the differences of differences are:
- 144 - 96 = 48
- 192 - 144 = 48
Pattern Identification
- The second-order differences are constant (48). This indicates a quadratic pattern.
- This suggests that the sequence follows a polynomial rule of degree 2.
Predicting the next term
- The next difference in the second-order differences will likely be 48.
- The next difference in the first-order differences would be 192 + 48 = 240
- The next term in the sequence would be 998 + 240 = 1238.
Conclusion
- Based on the observed pattern, the next number in the sequence is 1238.
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