| Exam Board | OCR |
|---|---|
| Module | C2 (Core Mathematics 2) |
| Year | 2006 |
| Session | June |
| Marks | 5 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Arithmetic Sequences and Series |
| Type | Periodic or repeating sequence |
| Difficulty | Moderate -0.8 This is a straightforward question requiring recognition of a periodic sequence with period 2. Part (i) involves simple substitution (u₂=-1, u₃=2, u₄=-1), and part (ii) requires counting 50 complete cycles of (2,-1) to get sum = 50. While it involves a recurrence relation, no complex reasoning is needed—just pattern recognition and basic arithmetic. |
| Spec | 1.04e Sequences: nth term and recurrence relations |
| Answer | Marks | Guidance |
|---|---|---|
| (i) \(u_2 = -1, u_1 = 2, u_4 = -1\) | B1, B1 | For correct value \(-1\) for \(u_2\). For correct values for both \(u_1\) and \(u_4\) |
| Answer | Marks | Guidance |
|---|---|---|
| i.e. \(50 \times (2 + (-1)) = 50\) | M1, M1, A1 | For correct interpretation of \(\Sigma\) notation. For pairing, or \(50 \times 2 - 50 \times 1\). For correct answer 50 |
**(i)** $u_2 = -1, u_1 = 2, u_4 = -1$ | B1, B1 | For correct value $-1$ for $u_2$. For correct values for both $u_1$ and $u_4$ | 2 marks
**(ii)** Sum is $(2 + (-1)) + (2 + (-1)) + \ldots + (2 + (-1))$
i.e. $50 \times (2 + (-1)) = 50$ | M1, M1, A1 | For correct interpretation of $\Sigma$ notation. For pairing, or $50 \times 2 - 50 \times 1$. For correct answer 50 | 3 marks
**Total: 5 marks**
---2 A sequence of terms $u _ { 1 } , u _ { 2 } , u _ { 3 } , \ldots$ is defined by
$$u _ { 1 } = 2 \quad \text { and } \quad u _ { n + 1 } = 1 - u _ { n } \text { for } n \geqslant 1 .$$
(i) Write down the values of $u _ { 2 } , u _ { 3 }$ and $u _ { 4 }$.\\
(ii) Find $\sum _ { n = 1 } ^ { 100 } u _ { n }$.
\hfill \mbox{\textit{OCR C2 2006 Q2 [5]}}