| Exam Board | OCR |
|---|---|
| Module | C2 (Core Mathematics 2) |
| Year | 2005 |
| Session | January |
| Marks | 7 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Arithmetic Sequences and Series |
| Type | Periodic or repeating sequence |
| Difficulty | Moderate -0.3 This is a straightforward recursive sequence question requiring simple substitution to find the pattern (part i), then recognizing the period-3 cycle to deduce u_200 (part ii). While it requires pattern recognition beyond pure recall, the calculations are trivial and the cyclic nature becomes obvious after computing just 3-4 terms, making this slightly easier than a typical A-level question. |
| Spec | 1.04e Sequences: nth term and recurrence relations |
2 A sequence $u _ { 1 } , u _ { 2 } , u _ { 3 } , \ldots$ is defined by
$$u _ { 1 } = 2 \quad \text { and } \quad u _ { n + 1 } = \frac { 1 } { 1 - u _ { n } } \text { for } n \geqslant 1 .$$
(i) Write down the values of $u _ { 2 } , u _ { 3 } , u _ { 4 }$ and $u _ { 5 }$.\\
(ii) Deduce the value of $u _ { 200 }$, showing your reasoning.
\hfill \mbox{\textit{OCR C2 2005 Q2 [7]}}