| Exam Board | AQA |
|---|---|
| Module | C2 (Core Mathematics 2) |
| Year | 2012 |
| Session | June |
| Marks | 5 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Arithmetic Sequences and Series |
| Type | Sum of first n terms |
| Difficulty | Moderate -0.8 This is a straightforward arithmetic series question requiring only direct application of standard formulas (common difference by inspection, nth term formula, and sum formula). All information is given explicitly, including the number of terms, making it easier than average with no problem-solving or insight required. |
| Spec | 1.04h Arithmetic sequences: nth term and sum formulae |
| Answer | Marks | Guidance |
|---|---|---|
| (common difference) \(= 9\) | B1 | CAO; answer is 9 |
| Answer | Marks | Guidance |
|---|---|---|
| \(100\text{th term} = 23 + (100-1)d = 914\) | M1, A1 | \(23 + (100-1)d\) or better seen (or used with \(d=9\) or with \(d=\) c's answer (a)); 914 NMS mark as B2 or B0 |
| Answer | Marks | Guidance |
|---|---|---|
| \(\text{Sum} = \frac{280}{2}(23 + 2534)\) or \(\frac{280}{2}[2\times23+(280-1)(9)]\) \(= 357980\) | M1, A1 | Substitution of \(n=280\), \(l=2534\), \(a=23\), \(d=9\) into \(\frac{n}{2}(a+l)\) or \(\frac{n}{2}[2a+(n-1)d]\); 357 980 NMS mark as B2 or B0 |
# Question 1:
## Part (a)
(common difference) $= 9$ | B1 | CAO; answer is 9
## Part (b)
$100\text{th term} = 23 + (100-1)d = 914$ | M1, A1 | $23 + (100-1)d$ or better seen (or used with $d=9$ or with $d=$ c's answer (a)); 914 NMS mark as B2 or B0
## Part (c)
$\text{Sum} = \frac{280}{2}(23 + 2534)$ or $\frac{280}{2}[2\times23+(280-1)(9)]$ $= 357980$ | M1, A1 | Substitution of $n=280$, $l=2534$, $a=23$, $d=9$ into $\frac{n}{2}(a+l)$ or $\frac{n}{2}[2a+(n-1)d]$; 357 980 NMS mark as B2 or B0
---1 The arithmetic series
$$23 + 32 + 41 + 50 + \ldots + 2534$$
has 280 terms.
\begin{enumerate}[label=(\alph*)]
\item Write down the common difference of the series.
\item Find the 100th term of the series.
\item Find the sum of the 280 terms of the series.
\end{enumerate}
\hfill \mbox{\textit{AQA C2 2012 Q1 [5]}}