Study Notes
A sequence is a list of numbers or objects arranged in a specific order. Sequences can be defined using rules that describe how to find the next term or any term in the sequence.
- Sequence — a list of numbers or objects in a special order. Example: 3, 5, 7, 9, ... is a sequence starting at 3 and increasing by 2 each time.
- Term-to-term rule — allows you to find the next number in the sequence if you know the previous term(s). Example: In the sequence 1, 3, 5, 7, ..., add 2 to the previous term to find the next term.
- Position-to-term rule — allows you to compute the value of any term in the sequence. Example: For the sequence 1, 3, 5, 7, ..., the nth term is given by a_n = 2n - 1.
- Arithmetic Sequence — a sequence made by adding the same value each time, called the "common difference." Example: 1, 4, 7, 10, ... is an arithmetic sequence with a common difference of 3.
Exam Tips
Key Definitions to Remember
- Sequence
- Term-to-term rule
- Position-to-term rule
- Arithmetic Sequence
Common Confusions
- Mixing up term-to-term and position-to-term rules
- Forgetting to apply the common difference consistently in arithmetic sequences
Typical Exam Questions
- What is the next term in the sequence 2, 4, 6, 8, ...? Answer: 10
- What is the 10th term of the sequence defined by a_n = 3n + 1? Answer: 31
- How do you find the common difference in the sequence 5, 10, 15, 20, ...? Answer: Subtract any term from the next term, e.g., 10 - 5 = 5
What Examiners Usually Test
- Ability to identify and apply term-to-term and position-to-term rules
- Understanding and calculating the common difference in arithmetic sequences