| Exam Board | OCR |
|---|---|
| Module | C2 (Core Mathematics 2) |
| Marks | 10 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Arithmetic Sequences and Series |
| Type | Sum of specific range of terms |
| Difficulty | Moderate -0.3 This is a straightforward arithmetic series question testing standard formulas and techniques. Part (a) requires direct application of the sum formula for an arithmetic series. Part (b) involves recall of the sum of first n integers formula and two routine applications with minor algebraic manipulation. All steps are mechanical with no problem-solving insight required, making it slightly easier than average but not trivial due to the multi-step nature and potential for arithmetic errors. |
| Spec | 1.04g Sigma notation: for sums of series1.04h Arithmetic sequences: nth term and sum formulae |
| Answer | Marks |
|---|---|
| AP: \(a = 27, l = 67\) | B1 |
| \(n = 30 - 9 = 21\) | B1 |
| \(S_{21} = \frac{21}{2}(27 + 67)\) | M1 |
| \(= \frac{21}{2} \times 94 = 987\) | A1 |
| Answer | Marks |
|---|---|
| \(\frac{1}{2}n(n+1)\) | B1 |
| Answer | Marks |
|---|---|
| \(= S_{300} - S_{99}\) | M1 |
| \(= \frac{1}{2} \times 200 \times 201 - \frac{1}{2} \times 99 \times 100\) | M1 |
| \(= 20100 - 4950 = 15150\) | A1 |
| Answer | Marks | Guidance |
|---|---|---|
| \(= 3 \times 15150 = 45450\) | M1 A1 | (10) |
## Part (a)
AP: $a = 27, l = 67$ | B1 |
$n = 30 - 9 = 21$ | B1 |
$S_{21} = \frac{21}{2}(27 + 67)$ | M1 |
$= \frac{21}{2} \times 94 = 987$ | A1 |
## Part (b)
### (i)
$\frac{1}{2}n(n+1)$ | B1 |
### (ii)
$= S_{300} - S_{99}$ | M1 |
$= \frac{1}{2} \times 200 \times 201 - \frac{1}{2} \times 99 \times 100$ | M1 |
$= 20100 - 4950 = 15150$ | A1 |
### (iii)
$= 3 \times 15150 = 45450$ | M1 A1 | (10)
---\begin{enumerate}[label=(\alph*)]
\item Evaluate
$$\sum_{r=10}^{30} (7 + 2r).$$ [4]
\item \begin{enumerate}[label=(\roman*)]
\item Write down the formula for the sum of the first $n$ positive integers. [1]
\item Using this formula, find the sum of the integers from 100 to 200 inclusive. [3]
\item Hence, find the sum of the integers between 300 and 600 inclusive which are divisible by 3. [2]
\end{enumerate}
\end{enumerate}
\hfill \mbox{\textit{OCR C2 Q7 [10]}}