| Exam Board | Edexcel |
|---|---|
| Module | C1 (Core Mathematics 1) |
| Marks | 7 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Arithmetic Sequences and Series |
| Type | Recurrence relation: find parameter from given term |
| Difficulty | Standard +0.3 This question involves straightforward substitution into a recurrence relation and basic algebraic manipulation. Part (a) requires calculator work with no conceptual challenge. Part (b)(i) involves solving a simple equation when two consecutive terms are equal, and (b)(ii) recognizes the sequence is constant. While recurrence relations may seem unfamiliar, the actual mathematical operations are routine for C1 level—significantly easier than typical multi-step problems requiring genuine problem-solving. |
| Spec | 1.04e Sequences: nth term and recurrence relations |
2. A sequence is defined by the recurrence relation $u _ { n + 1 } = \sqrt { \left( \frac { u _ { n } } { 2 } + \frac { a } { u _ { n } } \right) } , n = 1,2,3 , \ldots$, where $a$ is a constant.
\begin{enumerate}[label=(\alph*)]
\item Given that $a = 20$ and $u _ { 1 } = 3$, find the values of $u _ { 2 } , u _ { 3 }$ and $u _ { 4 }$, giving your answers to 2 decimal places.
\item Given instead that $u _ { 1 } = u _ { 2 } = 3$,
\begin{enumerate}[label=(\roman*)]
\item calculate the value of $a$,
\item write down the value of $u _ { 5 }$.
\end{enumerate}\end{enumerate}
\hfill \mbox{\textit{Edexcel C1 Q2 [7]}}