| Exam Board | OCR MEI |
|---|---|
| Module | C2 (Core Mathematics 2) |
| Year | 2010 |
| Session | June |
| Marks | 2 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Arithmetic Sequences and Series |
| Type | Recurrence relation: find specific terms |
| Difficulty | Easy -1.2 This is a straightforward iterative sequence question requiring only direct substitution of given values into a formula. The arithmetic involves simple fraction operations (division by 1 plus a fraction), which is routine for C2 level. No problem-solving insight is needed—just mechanical application of the recurrence relation three times. |
| Spec | 1.04e Sequences: nth term and recurrence relations |
| Answer | Marks |
|---|---|
| \([1], \frac{1}{2}, \frac{1}{3}, \frac{1}{4}\) | 2 marks |
$[1], \frac{1}{2}, \frac{1}{3}, \frac{1}{4}$ | 2 marks |You are given that
$$u_1 = 1,$$
$$u_{n+1} = \frac{u_n}{1 + u_n}.$$
Find the values of $u_2$, $u_3$ and $u_4$. Give your answers as fractions. [2]
\hfill \mbox{\textit{OCR MEI C2 2010 Q1 [2]}}