Study Notes
Sequences involve patterns of numbers that follow specific rules. They can be arithmetic, geometric, or based on special numbers like triangular, square, and cube numbers.
- Triangular Numbers — numbers that can be arranged in a triangle shape. Example: 1, 3, 6, 10, 15
- Square Numbers — numbers obtained by multiplying a number by itself. Example: 1, 4, 9, 16
- Cube Numbers — numbers obtained by multiplying a number by itself twice. Example: 1, 8, 27, 64
- Arithmetic Sequence — a sequence where each term is a fixed number more than the previous term. Example: 2, 4, 6, 8 (difference of 2)
- nth Term — a formula that allows you to find any term in a sequence. Example: For the sequence 6, 10, 14, 18, the nth term is 4n - 2.
Exam Tips
Key Definitions to Remember
- Triangular Numbers: Numbers that can be arranged in a triangle shape.
- Square Numbers: Numbers obtained by multiplying a number by itself.
- Cube Numbers: Numbers obtained by multiplying a number by itself twice.
- Arithmetic Sequence: A sequence where each term is a fixed number more than the previous term.
- nth Term: A formula to find any term in a sequence.
Common Confusions
- Confusing the formulas for triangular, square, and cube numbers.
- Mixing up the difference in arithmetic sequences with geometric sequences.
Typical Exam Questions
- What is the 5th triangular number? 15
- Find the nth term of the sequence 3, 6, 9, 12. 3n
- What is the 4th cube number? 64
What Examiners Usually Test
- Ability to generate terms from a given rule.
- Recognizing and using special sequences like triangular, square, and cube numbers.
- Deriving the nth term for linear sequences.