| Exam Board | OCR MEI |
|---|---|
| Module | C2 (Core Mathematics 2) |
| Year | 2013 |
| Session | June |
| Marks | 5 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Arithmetic Sequences and Series |
| Type | Sequence defined by formula |
| Difficulty | Easy -1.3 This is a straightforward arithmetic sequence question requiring only direct substitution to find terms, recognition of sequence type, and application of the standard arithmetic series formula. All steps are routine with no problem-solving or insight needed. |
| Spec | 1.04h Arithmetic sequences: nth term and sum formulae |
| Answer | Marks | Guidance |
|---|---|---|
| 11.5, 11 and 10.5 oe arithmetic and/or divergent | B1, B1 | allow AP; ignore labelling incorrect embellishments such as converging arithmetic..., diverging geometric... do not score. B0 if a choice is given eg AP/GP. |
| Answer | Marks | Guidance |
|---|---|---|
| \(n = 30\) identified as number of terms in relevant AP; \(S_{30} = \frac{30}{2}(2 \times 11.5 + (30-1) \times -0.5)\); \(127.5\) oe | B1, M1, A1 | or \(S_{30} = \frac{30}{2}(11.5 + -3)\); condone one error in \(a, d\) or \(n\) but do not condone \(l = -1/2\); allow recovery from slip in working (eg omission of minus sign); SC3 if each term calculated and summed to correct answer or for 127.5 unsupported |
### Part (i)
11.5, 11 and 10.5 oe arithmetic and/or divergent | B1, B1 | allow AP; ignore labelling incorrect embellishments such as converging arithmetic..., diverging geometric... do not score. B0 if a choice is given eg AP/GP.
### Part (ii)
$n = 30$ identified as number of terms in relevant AP; $S_{30} = \frac{30}{2}(2 \times 11.5 + (30-1) \times -0.5)$; $127.5$ oe | B1, M1, A1 | or $S_{30} = \frac{30}{2}(11.5 + -3)$; condone one error in $a, d$ or $n$ but do not condone $l = -1/2$; allow recovery from slip in working (eg omission of minus sign); SC3 if each term calculated and summed to correct answer or for 127.5 unsupportedThe $n$th term of a sequence, $u_n$, is given by
$$u_n = 12 - \frac{1}{2}n.$$
\begin{enumerate}[label=(\roman*)]
\item Write down the values of $u_1$, $u_2$ and $u_3$. State what type of sequence this is. [2]
\item Find $\sum_{n=1}^{30} u_n$. [3]
\end{enumerate}
\hfill \mbox{\textit{OCR MEI C2 2013 Q2 [5]}}