| Exam Board | OCR MEI |
|---|---|
| Module | C2 (Core Mathematics 2) |
| Marks | 5 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Geometric Sequences and Series |
| Type | Recursive sequence definition |
| Difficulty | Moderate -0.8 This is a straightforward geometric sequence question requiring only recognition of the sequence type, calculation of a term using the recurrence relation twice, and application of the standard sum to infinity formula. All steps are routine with no problem-solving or novel insight required, making it easier than average but not trivial since it involves multiple parts and the convergence condition. |
| Spec | 1.04e Sequences: nth term and recurrence relations1.04i Geometric sequences: nth term and finite series sum1.04j Sum to infinity: convergent geometric series |r|<1 |
| Answer | Marks | Guidance |
|---|---|---|
| (ii) mention of \( | r | < 1\) condition o.e. |
Question 2:
(i) 48
geometric, or GP
B1
B1
(ii) mention of $|r| < 1$ condition o.e.
B1
S = 128
M1 for $\frac{1}{1-(-\frac{1}{2})}$
A1
192
A12 The terms of a sequence are given by
$$\begin{aligned}
u _ { 1 } & = 192 , \\
u _ { n + 1 } & = - \frac { 1 } { 2 } u _ { n } .
\end{aligned}$$
(i) Find the third term of this sequence and state what type of sequence it is.\\
(ii) Show that the series $u _ { 1 } + u _ { 2 } + u _ { 3 } + \ldots$ converges and find its sum to infinity.
\hfill \mbox{\textit{OCR MEI C2 Q2 [5]}}