Study Notes
Sequences involve understanding how to describe and continue patterns using rules, such as finding the nth term or determining if a number is part of a sequence.
- Linear Sequence — a sequence where each term increases by a constant difference. Example: 6, 10, 14, 18 with nth term Un = 4n - 2.
- Quadratic Sequence — a sequence where the second difference between terms is constant. Example: 2, 7, 14, 23, 34 with nth term Un = n^2 + 2n - 1.
- Cubic Sequence — a sequence where the third difference between terms is constant. Example: 4, 16, 44, 94, 172, 284 with nth term Un = n^3 + 2n^2 - n + 2.
- Geometric Sequence — a sequence where each term is obtained by multiplying the previous term by a constant ratio. Example: 2, 6, 18, 54 with nth term Un = 2 x 3^(n-1).
- Arithmetic Sequence — a sequence where each term is obtained by adding a fixed quantity to the previous term. Example: 4, 12, 20, 28 with nth term Un = 8n - 4.
Exam Tips
Key Definitions to Remember
- Linear sequence: constant difference between terms.
- Quadratic sequence: constant second difference.
- Cubic sequence: constant third difference.
- Geometric sequence: constant ratio between terms.
- Arithmetic sequence: constant addition to each term.
Common Confusions
- Confusing the difference method for linear and quadratic sequences.
- Mixing up arithmetic and geometric sequences.
Typical Exam Questions
- What is the nth term of the sequence 4, 12, 20, 28? Answer: Un = 8n - 4
- Find the 500th term of the sequence 4, 12, 20, 28. Answer: 3996
- Which term of the sequence 4, 12, 20, 28 has the value 236? Answer: 30th term
What Examiners Usually Test
- Ability to find the nth term of a sequence.
- Understanding of the difference method for sequences.
- Application of sequences to solve problems involving specific terms.