| Exam Board | Edexcel |
|---|---|
| Module | C1 (Core Mathematics 1) |
| Marks | 4 |
| Paper | Download PDF ↗ |
| Topic | Sequences and Series |
| Type | Periodic Sequences |
| Difficulty | Moderate -0.8 This is a straightforward recursive sequence question requiring only direct substitution to find terms. Part (a) involves simple arithmetic (squaring small numbers), and part (b) requires recognizing that the sequence reaches a fixed point at u_2=4, making all subsequent terms equal to 4. No problem-solving insight or complex manipulation needed—purely mechanical calculation and pattern observation. |
| Spec | 1.04e Sequences: nth term and recurrence relations |
The sequence of positive numbers $u_1, u_2, u_3, \ldots$ is given by
$$u_{n+1} = (u_n - 3)^2, \quad u_1 = 1.$$
\begin{enumerate}[label=(\alph*)]
\item Find $u_2$, $u_3$ and $u_4$. [3]
\item Write down the value of $u_{20}$. [1]
\end{enumerate}
\hfill \mbox{\textit{Edexcel C1 Q2 [4]}}