| 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 is a straightforward recurrence relation question requiring substitution and basic algebraic manipulation. Part (a) involves simple calculator work iterating the formula. Part (b)(i) requires solving a simple equation when u₁ = u₂, and (b)(ii) recognizes the sequence is constant. While recurrence relations may seem unfamiliar, the actual mathematical operations are routine for C1 level, making this slightly easier than average. |
| Spec | 1.04e Sequences: nth term and recurrence relations |
(a) 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)
(b) Given instead that $u_1 = u_2 = 3$,
(i) calculate the value of $a$,
(3)
(ii) write down the value of $u_5$.
(1)\begin{enumerate}
\item A sequence is defined by the recurrence relation
\end{enumerate}
$$u _ { n + 1 } = \sqrt { \left( \frac { u _ { n } } { 2 } + \frac { a } { u _ { n } } \right) } , \quad n = 1,2,3 , \ldots ,$$
where $a$ is a constant.\\
(a) 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.\\
(b) Given instead that $u _ { 1 } = u _ { 2 } = 3$,\\
(i) calculate the value of $a$,\\
(ii) write down the value of $u _ { 5 }$.\\
\hfill \mbox{\textit{Edexcel C1 Q1 [7]}}