| Exam Board | OCR |
|---|---|
| Module | C2 (Core Mathematics 2) |
| Marks | 5 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Arithmetic Sequences and Series |
| Type | Sequence defined by formula |
| Difficulty | Moderate -0.8 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 only basic algebraic manipulation and no conceptual depth beyond understanding sequence notation. Easier than average for A-level. |
| Spec | 1.04e Sequences: nth term and recurrence relations |
\begin{enumerate}
\item The sequence $u _ { 1 } , u _ { 2 } , u _ { 3 } , \ldots$ is defined by
\end{enumerate}
$$u _ { n } = 2 ^ { n } + k n ,$$
where $k$ is a constant.\\
Given that $u _ { 1 } = u _ { 3 }$,\\
(i) find the value of $k$,\\
(ii) find the value of $u _ { 5 }$.\\
\hfill \mbox{\textit{OCR C2 Q1 [5]}}