| Exam Board | Edexcel |
|---|---|
| Module | C1 (Core Mathematics 1) |
| Marks | 7 |
| Paper | Download PDF ↗ |
| Topic | Sequences and Series |
| Type | Convergence and Limits of Sequences |
| Difficulty | Standard +0.3 This is a straightforward recurrence relation question requiring substitution and basic algebraic manipulation. Part (a) involves simple calculator work iterating the formula. Part (b) uses the condition u₁=u₂ to solve for 'a' by setting up and solving a simple equation, then recognizing the sequence is constant. While it requires careful algebra, it's a standard C1-level exercise with no novel insight needed. |
| Spec | 1.02b Surds: manipulation and rationalising denominators1.04e Sequences: nth term and recurrence relations |
A sequence is defined by the recurrence relation
$$u_{n+1} = \sqrt{\frac{u_n}{2} + \frac{a}{u_n}}, \quad n = 1, 2, 3, \ldots,$$
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. [3]
\item Given instead that $u_1 = u_2 = 3$,
\begin{enumerate}[label=(\roman*)]
\item calculate the value of $a$, [3]
\item write down the value of $u_5$. [1]
\end{enumerate}
\end{enumerate}
\hfill \mbox{\textit{Edexcel C1 Q38 [7]}}