Study Notes
Sequences are ordered lists of numbers following specific patterns. Linear Sequence — a sequence where the difference between consecutive terms is constant. Example: 6, 10, 14, 18 with a 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, 13.
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 each term is a triangular number.
- Fibonacci Sequence: A sequence where each term is the sum of the two preceding terms.
Common Confusions
- Confusing the first and second differences in sequences.
- Misapplying the formula for triangular numbers.
Typical Exam Questions
- What is the nth term of the sequence 6, 10, 14, 18? Un = 4n - 2
- How do you find the 10th triangular number? Use the formula n(n+1)/2
- What is the next term in the Fibonacci sequence 0, 1, 1, 2, 3, 5? 8
What Examiners Usually Test
- Ability to identify and calculate terms in different types of sequences.
- Understanding of how to derive formulas for sequences.
- Application of sequence rules to solve problems.