Summary
Sequences in mathematics involve understanding patterns and rules that define the order of numbers. You can generate sequences using term-to-term or position-to-term rules and find the nth term of linear sequences.
- Square Numbers — numbers obtained by multiplying a number by itself.
Example: The 2nd square number is 2 x 2 = 4. - Cube Numbers — numbers obtained by multiplying a number by itself twice.
Example: The 3rd cube number is 3 x 3 x 3 = 27. - Triangular Numbers — numbers that can be arranged in a triangular shape.
Example: The 4th triangular number is 1 + 2 + 3 + 4 = 10. - Linear Sequence — a sequence where the difference between consecutive terms is constant.
Example: In the sequence 6, 10, 14, 18, the difference is +4.
Exam Tips
Key Definitions to Remember
- Square Numbers: n x n = n^2
- Cube Numbers: n x n x n = n^3
- Triangular Numbers: n(n+1)/2
- Linear Sequence: A sequence with a constant difference between terms
Common Confusions
- Confusing square numbers with cube numbers
- Miscalculating the nth term in a linear sequence
Typical Exam Questions
- What is the 5th square number?
Answer: 25 - How do you find the nth term of the sequence 6, 10, 14, 18?
Answer: U_n = 4n - 2 - What is the 3rd triangular number?
Answer: 6
What Examiners Usually Test
- Ability to generate terms from a given rule
- Understanding and application of formulas for square, cube, and triangular numbers
- Calculation of the nth term in linear sequences