| Exam Board | Edexcel |
|---|---|
| Module | C1 (Core Mathematics 1) |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Arithmetic Sequences and Series |
| Type | Recurrence relation: find specific terms |
| Difficulty | Moderate -0.8 This is a straightforward recurrence relation requiring simple substitution and arithmetic. Part (a) involves three direct calculations using the formula, and part (b) requires recognizing that the sequence reaches a fixed point at u₃=4 (since (4-3)²=1 and (1-3)²=4 creates a cycle). This is easier than average as it's purely computational with minimal problem-solving, though slightly more involved than basic index law recall. |
| Spec | 1.04e Sequences: nth term and recurrence relations |
| Answer | Marks | Guidance |
|---|---|---|
| Answer/Working | Marks | Guidance |
| (a) \(32^{\frac{1}{5}}=2\) | B1 | Answer 2 must be in part (a) for this mark |
| (b) \(2^{-2}\) or \(\frac{1}{4}\) or \(\left(\frac{1}{2}\right)^2\) or \(0.25\) as coefficient of \(x^k\) | M1 | For \(2^{-2}\) or \(\frac{1}{4}\) or \(\left(\frac{1}{2}\right)^2\) or \(0.25\) in answer as coefficient of \(x^k\) for any numerical value of \(k\) (including \(k=0\)) |
| Correct index: \(Ax^{-2}\) or \(\frac{A}{x^2}\) | B1 | \(Ax^{-2}\) or \(\frac{A}{x^2}\) or equivalent e.g. \(Ax^{-\frac{10}{5}}\); correct power of \(x\) seen in final answer |
| \(= \frac{1}{4x^2}\) or \(0.25x^{-2}\) | A1 cao | Must be correct power and coefficient combined correctly; must not be followed by a different wrong answer |
## Question 2:
| Answer/Working | Marks | Guidance |
|---|---|---|
| (a) $32^{\frac{1}{5}}=2$ | B1 | Answer 2 must be in part (a) for this mark |
| (b) $2^{-2}$ or $\frac{1}{4}$ or $\left(\frac{1}{2}\right)^2$ or $0.25$ as coefficient of $x^k$ | M1 | For $2^{-2}$ or $\frac{1}{4}$ or $\left(\frac{1}{2}\right)^2$ or $0.25$ in answer as coefficient of $x^k$ for any numerical value of $k$ (including $k=0$) |
| Correct index: $Ax^{-2}$ or $\frac{A}{x^2}$ | B1 | $Ax^{-2}$ or $\frac{A}{x^2}$ or equivalent e.g. $Ax^{-\frac{10}{5}}$; correct power of $x$ seen in final answer |
| $= \frac{1}{4x^2}$ or $0.25x^{-2}$ | A1 cao | Must be correct power **and** coefficient combined correctly; must not be followed by a different wrong answer |
---2. The sequence of positive numbers $u _ { 1 } , u _ { 2 } , u _ { 3 } , \ldots$ is given by:
$$u _ { n + 1 } = \left( u _ { n } - 3 \right) ^ { 2 } , \quad u _ { 1 } = 1$$
\begin{enumerate}[label=(\alph*)]
\item Find $u _ { 2 } , u _ { 3 }$ and $u _ { 4 }$.
\item Write down the value of $u _ { 20 }$.
\end{enumerate}
\hfill \mbox{\textit{Edexcel C1 Q2}}