| Exam Board | OCR MEI |
|---|---|
| Module | C2 (Core Mathematics 2) |
| Year | 2006 |
| Session | June |
| Marks | 5 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Arithmetic Sequences and Series |
| Type | Sum of specific range of terms |
| Difficulty | Moderate -0.8 This is a straightforward arithmetic sequence question requiring basic pattern recognition and application of standard formulas. Part (i) is trivial substitution, and part (ii) requires finding the 51st and 100th terms then using the sum formula—all routine procedures with no problem-solving insight needed. The 5 marks reflect mechanical steps rather than conceptual difficulty. |
| Spec | 1.04h Arithmetic sequences: nth term and sum formulae |
| Answer | Marks | Guidance |
|---|---|---|
| (i) \(3, 8, 13, 18\) | B1 | Ignore extras |
| (ii) use of \(n/2[2a + (n-1)d]\) | M1 | Use of \(a + (n-1)d\) |
| \(S_{151} = 253\) \(u_{100} = 498\) | M1 | |
| \(S_{50} = 248\) \(u_{52} = 258\) | M1 | |
| 50/2(their(\(u_{51} + u_{100}\))) dep't on M1 or 50/[2 × their(\(u_{51} + 49 ×\))] | M1 A1 | |
| \(18 775\) cao | A1 |
(i) $3, 8, 13, 18$ | B1 | Ignore extras |
(ii) use of $n/2[2a + (n-1)d]$ | M1 | Use of $a + (n-1)d$ |
$S_{151} = 253$ $u_{100} = 498$ | M1 | |
$S_{50} = 248$ $u_{52} = 258$ | M1 | |
50/2(their($u_{51} + u_{100}$)) dep't on M1 or 50/[2 × their($u_{51} + 49 ×$)] | M1 A1 | |
$18 775$ cao | A1 | | $5$ |A sequence is given by the following.
$$u_1 = 3$$
$$u_{n+1} = u_n + 5$$
\begin{enumerate}[label=(\roman*)]
\item Write down the first 4 terms of this sequence. [1]
\item Find the sum of the 51st to the 100th terms, inclusive, of the sequence. [4]
\end{enumerate}
\hfill \mbox{\textit{OCR MEI C2 2006 Q6 [5]}}