Higher November 2024 Paper 4 Q18
18 Some sequences are defined using this term-to-term rule.
\(u_{n+1} = 5u_n - 8\).
(a) If \(u_3 = 22\), show that \(u_4 = 102\). [1]
(b) If \(u_3 = 22\), work out \(u_2\). [3]
(c) If \(u_1 = 2\), write down the value of \(u_{50}\).
Give a reason for your answer. [2]
Give a reason for your answer. [2]
| Answer | Marks | Part marks and guidance | |
|---|---|---|---|
| 5 × 22 – 8 or \(\frac{102 + 8}{5} = 22\) oe | M1 | Condone 110 – 8 or \(5u_3 - 8 = 102\) then \(5u_3 = 110\) then \(u_3 = 22\) | |
| Answer | Marks | Part marks and guidance | |
|---|---|---|---|
| 6 | 3 | M2 for \(\frac{22 + 8}{5}\) or better or M1 for \(u_3 = 5u_2 - 8\) or better | e.g. M2 for \(\frac{30}{5}\) e.g. M1 for \(22 = 5u_2 - 8\) |
| Answer | Marks | Part marks and guidance | |
|---|---|---|---|
| 2 | B1 | ||
| \(u_2 = u_1\), so all terms will be equal | B1 | If 0 scored SC1 for next term = 2 or 5 × 2 – 8 seen | |
Appendix: Exemplar responses for Q18(c)
| Response | Mark |
|---|---|
| \(u_2 = u_1\), so all terms will be equal | 1 |
| every term is 2 | 1 |
| repeats [infinitely] | 1 |
| because \(u_2 = 2\) | 0 |
| because \(u_2\) equals \(u_1\) | 0 |