| Exam Board | AQA |
|---|---|
| Module | C2 (Core Mathematics 2) |
| Year | 2009 |
| Session | June |
| Marks | 7 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Sequences and series, recurrence and convergence |
| Type | Linear iterative formula u(n+1) = pu(n) + q |
| Difficulty | Moderate -0.3 This is a straightforward recurrence relation question requiring substitution to find k, iteration to find subsequent terms, and understanding that at the limit L = kL + 12. All parts follow standard procedures with no novel insight needed, making it slightly easier than average but still requiring multiple techniques. |
| Spec | 1.04e Sequences: nth term and recurrence relations |
The $n$th term of a sequence is $u_n$.
The sequence is defined by
$$u_{n+1} = ku_n + 12$$
where $k$ is a constant.
The first two terms of the sequence are given by
$$u_1 = 16 \quad u_2 = 24$$
\begin{enumerate}[label=(\alph*)]
\item Show that $k = 0.75$. [2]
\item Find the value of $u_3$ and the value of $u_4$. [2]
\item The limit of $u_n$ as $n$ tends to infinity is $L$.
\begin{enumerate}[label=(\roman*)]
\item Write down an equation for $L$. [1]
\item Hence find the value of $L$. [2]
\end{enumerate}
\end{enumerate}
\hfill \mbox{\textit{AQA C2 2009 Q3 [7]}}