Higher June 2025 Paper 3 Q18
18 Here are the first four terms of a quadratic sequence.
6 \(\qquad\quad\) 15 \(\qquad\quad\) 28 \(\qquad\quad\) 45
Work out an expression for the \(n\)th term. [3 marks]
| Answer | Mark | Comments |
|---|---|---|
| \(2n^2 + 3n + 1\) or \(a = 2\) and \(b = 3\) and \(c = 1\) | B3 | B2 \(2n^2 + 3n\ (+\,c)\) or \(a = 2\) and \(b = 3\) or \(2n^2\ (+\,bn) + 1\) or \(a = 2\) and \(c = 1\) B1 \(2n^2\ (+\,bn + c)\) or \(a = 2\) or \(an^2\ (+\,bn) + 1\) with \(a \ne 0\) or \(c = 1\) or second difference = 4 |
Additional guidance
| Terms may be in any order | |
| Second difference = 4 scores B1 even if used incorrectly eg answer \(8n\) | |
| 4 must be the second difference to score B1 eg answer \(5n + 4\) with no working or statement that 4 is the second difference | B0 |
| Condone \(n = 2n^2 + 3n + 1\) | B3 |
| Condone \(2n^2 + 3n + 1 = 0\) | B2 |
| Condone \(2x^2 - 5\) etc | B1 |