| Exam Board | Edexcel |
|---|---|
| Module | C1 (Core Mathematics 1) |
| Marks | 5 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Arithmetic Sequences and Series |
| Type | Sequence defined by formula |
| Difficulty | Moderate -0.5 This is a straightforward substitution problem requiring students to evaluate the formula at n=1 and n=3, set them equal, solve for k, then substitute into n=5. It involves basic algebraic manipulation and index laws but is more routine than average, requiring no problem-solving insight beyond direct application of the given formula. |
| Spec | 1.04e Sequences: nth term and recurrence relations |
| Answer | Marks | Guidance |
|---|---|---|
| (a) \(u_1 = 2 + k\) | B1 | |
| \(u_3 = 8 + 3k\) | M1 | |
| \(u_1 = u_3\) ⇒ \(2 + k = 8 + 3k\) | A1 | |
| \(k = -3\) | ||
| (b) \(u_5 = 2^5 - 3(5) = 32 - 15 = 17\) | M1 A1 | (5 marks) |
**(a)** $u_1 = 2 + k$ | B1 |
$u_3 = 8 + 3k$ | M1 |
$u_1 = u_3$ ⇒ $2 + k = 8 + 3k$ | A1 |
$k = -3$ | |
**(b)** $u_5 = 2^5 - 3(5) = 32 - 15 = 17$ | M1 A1 | (5 marks)3. The sequence $u _ { 1 } , u _ { 2 } , u _ { 3 } , \ldots$ is defined by
$$u _ { n } = 2 ^ { n } + k n ,$$
where $k$ is a constant.
Given that $u _ { 1 } = u _ { 3 }$,
\begin{enumerate}[label=(\alph*)]
\item find the value of $k$,
\item find the value of $u _ { 5 }$.
\end{enumerate}
\hfill \mbox{\textit{Edexcel C1 Q3 [5]}}