Higher November 2018 Paper 1 Q21
21 Here are the first four terms of a quadratic sequence.
\[11 \qquad 26 \qquad 45 \qquad 68\]Work out an expression for the \(n\)th term. [3 marks]
| Answer | Mark | Comments |
|---|---|---|
| Alternative method 1 | ||
| (second differences =) 4 or \(2n^2\) or \(a = 2\) | M1 | second difference seen at least once and not contradicted |
| \(11 - 2 \times 1^2\) and \(26 - 2 \times 2^2\) and \(45 - 2 \times 3^2\) (and \(68 - 2 \times 4^2\)) or 9 and 18 and 27 (and 36) or \(9n\) | M1dep | |
| \(2n^2 + 9n\) | A1 | oe |
| Alternative method 2 | ||
| any two of \(a + b + c = 11\) \(4a + 2b + c = 26\) \(9a + 3b + c = 45\) \(16a + 4b + c = 68\) | M1 | |
| \(3a + b = 26 - 11\) and \(5a + b = 45 - 26\) or \(a = 2\) and \(b = 9\) (and \(c = 0\)) | M1dep | oe obtains two correct equations in same two variables from their equations |
| \(2n^2 + 9n\) | A1 | oe |
| Alternative method 3 | ||
| (second differences =) 4 or \(2n^2\) or \(a = 2\) | M1 | second difference seen at least once and not contradicted |
| \(3a + b = 26 - 11\) and substitutes \(a = 2\) or \(b = 9\) or \(9n\) | M1dep | |
| \(2n^2 + 9n\) | A1 | oe |