June 2024 Paper 1 Q23
23 The \(n\)th term of a quadratic sequence is \(\quad an^2 - 5n + c \quad\) where \(a\) and \(c\) are integers.
The first four terms of the sequence are
\(\qquad 2 \qquad x \qquad 16 \qquad y\)
Work out the values of \(x\) and \(y\). [5 marks]
| Answer | Mark | Comments |
|---|---|---|
| \(x = 6\) and \(y = 32\) | B5 | B4 \(x = 6\) or \(y = 32\) and \(a = 3\) or \(c = 4\) (could be embedded in \(3n^2 - 5n + 4\)) B3 \(a = 3\) or \(c = 4\) (could be embedded in \(3n^2 - 5n + 4\)) B2 any two different correct equations set up for a combination of \(a\), \(c\), \(x\) and \(y\) (may include \(b\). Do not include \(b = -5\)) B1 any correct equation set up for a combination of \(a\), \(c\), \(x\) and \(y\) (may include \(b\). Do not include \(b = -5\)) or (second difference) \(= 18 - 2x\) or \(x + y - 32\) (must be correctly simplified) |
Additional guidance
| Do not accept any equations with \(n\) | |
| \(x = 6\) on answer line with no working and \(y \ne 32\) | B0 |
| \(x = 6\) and \(y = 32\) on answer line with no working | B5 |