Summary
A sequence is a list of numbers or objects arranged in a specific order. Sequences can be defined using rules that determine 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 an = 2n - 1.
- Arithmetic Sequence — a sequence made by adding the same value each time, known as the "common difference." Example: In the sequence 1, 4, 7, 10, ..., the common difference is 3.
Exam Tips
Key Definitions to Remember
- Sequence
- Term-to-term rule
- Position-to-term rule
- Arithmetic Sequence
- Common difference
Common Confusions
- Confusing term-to-term and position-to-term rules
- Forgetting to apply the common difference consistently
Typical Exam Questions
- What is the next term in the sequence 2, 4, 6, 8, ...? Add 2 to the last term: 10
- What is the 10th term of the sequence 3, 6, 9, 12, ...? Use the nth term formula: 3n, so 3(10) = 30
- What is the common difference in the sequence 5, 10, 15, 20, ...? The common difference is 5
What Examiners Usually Test
- Ability to identify the next term using a term-to-term rule
- Calculation of any term using a position-to-term rule
- Understanding and identifying the common difference in arithmetic sequences