| Exam Board | OCR |
|---|---|
| Module | C2 (Core Mathematics 2) |
| Marks | 5 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Arithmetic Sequences and Series |
| Type | Recurrence relation: find parameter from given term |
| Difficulty | Moderate -0.8 Part (i) requires simple substitution into a formula (n=1,2,3,4), which is routine arithmetic. Part (ii) involves finding constants in a recurrence relation by substituting consecutive terms and solving simultaneous equations—a standard technique but requires some algebraic manipulation. Overall, this is easier than average as it's mostly procedural with no conceptual challenges or novel problem-solving required. |
| Spec | 1.04e Sequences: nth term and recurrence relations |
\begin{enumerate}
\item A sequence of terms is defined by
\end{enumerate}
$$u _ { n } = 3 ^ { n } - 2 , \quad n \geq 1 .$$
(i) Write down the first four terms of the sequence.
The same sequence can also be defined by the recurrence relation
$$u _ { n + 1 } = a u _ { n } + b , \quad n \geq 1 , \quad u _ { 1 } = 1 ,$$
where $a$ and $b$ are constants.\\
(ii) Find the values of $a$ and $b$.\\
\hfill \mbox{\textit{OCR C2 Q1 [5]}}