| Exam Board | OCR MEI |
|---|---|
| Module | C2 (Core Mathematics 2) |
| Marks | 5 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Arithmetic Sequences and Series |
| Type | Find n given sum condition |
| Difficulty | Moderate -0.3 This is a straightforward two-part question on arithmetic progressions requiring basic formula application. Part (i) is trivial subtraction; part (ii) involves substituting into the sum formula and solving a quadratic inequality, which is standard C2 content but requires careful algebraic manipulation to find when S_n < 0. |
| Spec | 1.04h Arithmetic sequences: nth term and sum formulae1.04i Geometric sequences: nth term and finite series sum |
| Answer | Marks | Guidance |
|---|---|---|
| \(d = 5.9 - 7 = -1.1\) | B1 | Total: 1 |
| Answer | Marks | Guidance |
|---|---|---|
| For negative sum, \(14-(n-1)1.1 < 0\) | M1 A1 | |
| \(\Rightarrow n-1 > \frac{1.4}{1.1} \Rightarrow n-1 > 12.7...\) | A1 | |
| \(\Rightarrow n > 13.7\) i.e. \(n \geq 14\), \((S_{13} = 5.2,\ S_{14} = -2.1)\) | A1 | Total: 4 |
## Question 4(i):
$d = 5.9 - 7 = -1.1$ | B1 | **Total: 1**
## Question 4(ii):
For negative sum, $14-(n-1)1.1 < 0$ | M1 A1 |
$\Rightarrow n-1 > \frac{1.4}{1.1} \Rightarrow n-1 > 12.7...$ | A1 |
$\Rightarrow n > 13.7$ i.e. $n \geq 14$, $(S_{13} = 5.2,\ S_{14} = -2.1)$ | A1 | **Total: 4**
---4 The first 3 terms of an arithmetical progression are 7, 5.9 and 4.8.\\
Find\\
(i) the common difference,\\
(ii) the smallest value of $n$ for which the sum to $n$ terms is negative.
\hfill \mbox{\textit{OCR MEI C2 Q4 [5]}}