Higher November 2019 Paper 6 Q11
11 A sequence is defined by the rule \(u_{n+1} = 5u_n - 15\).
(a) If \(u_3 = 6\), calculate
(i) \(u_5\) [3]
(ii) \(u_2\) [3]
(b) Trevor says
If \(u_1 = 3.75\) then \(u_{100} = 3.75\)
Show that Trevor is correct. [2]
| Answer | Marks | Part marks and guidance | |
|---|---|---|---|
| (i) 60 | 3 | B2 for [\(u_4\) =] 15 or M1 for 5 × 6 – 15 | |
| (ii) 4.2 oe | 3 | M2 for (6 + 15) ÷ 5 or M1 for \(6 = 5u_2 - 15\) or \(u_2 = \frac{u_3 + 15}{5}\) | Allow \(6 = 5k - 15\) or \(u_n = \frac{u_{n+1} + 15}{5}\) |
| Answer | Marks | Part marks and guidance | |
|---|---|---|---|
| [\(u_2\) =] 5 × 3.75 – 15 = 3.75 | 1 | Must see calculation and answer | |
| Since \(u_1 = u_2\), all terms are equal | 1dep | Accept “every term is 3.75” | |