| Exam Board | OCR |
|---|---|
| Module | C2 (Core Mathematics 2) |
| 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 to find u₂ and u₃, then solving a polynomial equation. While it involves algebraic manipulation and solving a quartic that factors nicely, it's a standard C2 exercise with clear steps and no novel insight required—slightly easier than average. |
| Spec | 1.04e Sequences: nth term and recurrence relations |
3. The sequence $u _ { 1 } , u _ { 2 } , u _ { 3 } , \ldots$ is defined by
$$u _ { n + 1 } = \left( u _ { n } \right) ^ { 2 } - 1 , \quad n \geq 1 .$$
Given that $u _ { 1 } = k$, where $k$ is a constant,\\
(i) find expressions for $u _ { 2 }$ and $u _ { 3 }$ in terms of $k$.
Given also that $u _ { 2 } + u _ { 3 } = 11$,\\
(ii) find the possible values of $k$.\\
\hfill \mbox{\textit{OCR C2 Q3 [7]}}