Study Notes
Sequences are ordered lists of numbers following a specific pattern. They can be linear, quadratic, triangular, or Fibonacci.
- Linear Sequence — A sequence where the difference between consecutive terms is constant. Example: 6, 10, 14, 18 with a common difference of 4.
- Quadratic Sequence — A sequence where the second difference between terms is constant. Example: 2, 7, 14, 23, 34 with a second difference of 2.
- Triangular Number Sequence — A sequence where each term represents a triangular number. Example: 1, 3, 6, 10, calculated using n(n+1)/2.
- Fibonacci Sequence — A sequence where each term is the sum of the two preceding ones. Example: 0, 1, 1, 2, 3, 5, 8.
Exam Tips
Key Definitions to Remember
- Linear Sequence: A sequence with a constant difference between terms.
- Quadratic Sequence: A sequence with a constant second difference.
- Triangular Number Sequence: A sequence where terms are triangular numbers.
- Fibonacci Sequence: A sequence where each term is the sum of the two preceding terms.
Common Confusions
- Confusing linear and quadratic sequences due to their differences.
- Forgetting the formula for triangular numbers.
Typical Exam Questions
- What is the nth term of a linear sequence? Use the formula Un = an + b.
- How do you find the nth term of a quadratic sequence? Use the formula Un = an^2 + bn + c.
- How do you calculate a triangular number? Use the formula n(n+1)/2.
What Examiners Usually Test
- Ability to find the general term of a sequence.
- Understanding the difference between sequence types.
- Application of formulas to calculate specific terms.