Higher November 2021 Paper 4 Q15
15 Here are the first four terms of a quadratic sequence.
−1 3 13 29
The \(n\)th term is \(an^2 + bn + c\).
Find the values of \(a\), \(b\) and \(c\). [4]
| Answer | Marks | Part marks and guidance | |
|---|---|---|---|
| [a=] 3 [b=] −5 [c=] 1 | 4 | B2 for a = 3 or M1 for second differences = 6 M1 for revised terms of −4 −9 −14 −19 or B1 for either b = −5 or c = 1 | Condone e.g. \(3n^2\) at least two terms See appendix for alternative methods |
Appendix: Question 15
Using simultaneous equations : e.g.
\(a + b + c = -1\)
\(4a + 2b + c = 3\)
\(9a + 3b + c = 13\) ………M1
subtracting
\(3a + b = 4\)
\(5a + b = 10\) …….. M1
gives \(a = 3\) ………..A1