| Exam Board | OCR MEI |
|---|---|
| Module | C2 (Core Mathematics 2) |
| Marks | 5 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Sequences and Series |
| Type | Sequence Behaviour Classification |
| Difficulty | Standard +0.3 This question requires computing several terms of recursively-defined sequences and identifying their behavior (convergent/divergent/periodic), which is straightforward calculation with basic pattern recognition. While it involves three parts and requires understanding of sequence behavior, the computations are simple arithmetic and the patterns become clear quickly—no proof or deep insight required, making it slightly easier than average. |
| Spec | 1.04e Sequences: nth term and recurrence relations1.04f Sequence types: increasing, decreasing, periodic8.01a Recurrence relations: general sequences, closed form and recurrence8.01c Sequence behaviour: periodic, convergent, divergent, oscillating, monotonic8.01d Sequence limits: limit of nth term as n tends to infinity, steady-states |
| Answer | Marks | Guidance |
|---|---|---|
| (i) -1, -4, -1, -4 Periodic | B1 B1 | 2 marks |
| (ii) \(1, 1\frac{1}{2}, 1\frac{3}{4},...\) Convergent to 2 | B1 B1 | 2 marks |
| (iii) 0.1, 4, 25, ... Divergent | B1 | 1 mark |
**(i)** -1, -4, -1, -4 Periodic | B1 B1 | 2 marks
**(ii)** $1, 1\frac{1}{2}, 1\frac{3}{4},...$ Convergent to 2 | B1 B1 | 2 marks
**(iii)** 0.1, 4, 25, ... Divergent | B1 | 1 mark7 For each of the following sequences, write down sufficient terms of the sequence in order to be able to describe its behaviour as divergent, periodic or convergent. For any convergent sequence, state its limit.\\
(i) $a _ { 1 } = - 1 ; \quad a _ { k + 1 } = \frac { 4 } { a _ { k } }$\\
(ii) $\quad a _ { 1 } = 1 ; \quad a _ { k } = 2 - 2 \times \left( \frac { 1 } { 2 } \right) ^ { k }$\\
(iii) $\quad a _ { 1 } = 0 \quad a _ { k + 1 } = \left( 1 + a _ { k } \right) ^ { 2 }$.
\hfill \mbox{\textit{OCR MEI C2 Q7 [5]}}