Study Notes
A sequence is a list of numbers or objects in a special order.
- 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. 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. Example: 1, 4, 7, 10, ... is an arithmetic sequence with a common difference of 3.
Exam Tips
Key Definitions to Remember
- Sequence: A list of numbers or objects in a special order.
- Term to term rule: A rule to find the next number in a sequence using the previous term.
- Position to term rule: A rule to compute the value of any term in the sequence.
- Arithmetic Sequence: A sequence made by adding the same value each time.
Common Confusions
- Confusing the term to term rule with the position to term rule.
- 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 3, 6, 9, ...? Answer: 30
- How do you find the nth term of the sequence 5, 10, 15, ...? Answer: a_n = 5n
What Examiners Usually Test
- Understanding of how to find the next term in a sequence.
- Ability to derive the nth term formula for a sequence.
- Application of the common difference in arithmetic sequences.