| Exam Board | Edexcel |
|---|---|
| Module | C1 (Core Mathematics 1) |
| Year | 2006 |
| Session | January |
| Marks | 4 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Arithmetic Sequences and Series |
| Type | Periodic or repeating sequence |
| Difficulty | Moderate -0.8 This is a straightforward recursive sequence question requiring simple arithmetic calculations. Part (a) involves three direct substitutions with basic operations (subtraction and squaring). Part (b) requires recognizing the pattern repeats (1→4→1), making u_20 trivial to find. No problem-solving insight needed beyond pattern recognition, making it easier than average C1 material. |
| Spec | 1.04e Sequences: nth term and recurrence relations |
| Answer | Marks |
|---|---|
| (a) \(u_2 = (-2)^2 = 4\) | B1 |
| \(u_3 = 1, u_4 = 4\) for \(u_3\), ft \((u_2-3)^2\) | B1ft, B1 |
| (b) \(u_{30} = 4\) | B1ft |
| Answer | Marks |
|---|---|
| Guidance: (b) ft only if sequence is "oscillating". Do not give marks if answers have clearly been obtained from wrong working, e.g. \(u_2 = (3-3)^2 = 0\), \(u_3 = (4-3)^2 = 1\), \(u_4 = (5-3)^2 = 4\). |
**(a)** $u_2 = (-2)^2 = 4$ | B1 |
$u_3 = 1, u_4 = 4$ for $u_3$, ft $(u_2-3)^2$ | B1ft, B1 |
**(b)** $u_{30} = 4$ | B1ft |
**Total: 4 marks**
| Guidance: (b) ft only if sequence is "oscillating". Do not give marks if answers have clearly been obtained from wrong working, e.g. $u_2 = (3-3)^2 = 0$, $u_3 = (4-3)^2 = 1$, $u_4 = (5-3)^2 = 4$.
---2. The sequence of positive numbers $u _ { 1 } , u _ { 2 } , u _ { 3 } , \ldots$ is given by:
$$u _ { n + 1 } = \left( u _ { n } - 3 \right) ^ { 2 } , \quad u _ { 1 } = 1 .$$
\begin{enumerate}[label=(\alph*)]
\item Find $u _ { 2 } , u _ { 3 }$ and $u _ { 4 }$.
\item Write down the value of $u _ { 20 }$.
\end{enumerate}
\hfill \mbox{\textit{Edexcel C1 2006 Q2 [4]}}