Algebraic Reasoning and Patterns
What you must understand
This domain tests recognising and continuing sequences, writing and simplifying expressions, substituting values, solving linear equations, and using formulas. You should be able to find the nth term of a linear sequence, spot patterns in number and shape sequences, and rearrange simple formulas.
Traps to watch for
- Sign errors when substituting: if x = -2, then x² = 4 but 3x = -6. Substitute with brackets to stay safe.
- Collecting unlike terms: 3a + 2b cannot be simplified to 5ab.
- nth term offset: for the sequence 5, 8, 11, ... the common difference is 3, so the nth term is 3n + 2, not 3n.
- Solving equations: whatever you do to one side, do to the other; when dividing by a negative, the inequality sign flips.
- Rearranging formulas: undo operations in reverse order, treating the target variable as the subject.
Worked example
Find the nth term of 4, 9, 14, 19, ... and the 20th term. The common difference is 5, so the term is 5n + c. For n = 1, 5(1) + c = 4, so c = -1. nth term = 5n − 1. The 20th term = 5(20) − 1 = 99.
Rule of thumb: common difference × n, then adjust by comparing the first term with the difference.