| Exam Board | AQA |
|---|---|
| Module | C2 (Core Mathematics 2) |
| Year | 2008 |
| Session | January |
| 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 series question requiring only direct application of standard formulas. Part (a) is immediate observation, part (b) uses the nth term formula with given information, and part (c) applies the sum formula. All steps are routine with no problem-solving insight needed, making it easier than average. |
| Spec | 1.04h Arithmetic sequences: nth term and sum formulae |
| Answer | Marks | Guidance |
|---|---|---|
| Working | Mark | Guidance |
| \((d) = 7\) | B1 | 7 — Total: 1 |
| Answer | Marks | Guidance |
|---|---|---|
| Working | Mark | Guidance |
| \((101^\text{st}\text{ term}) = a + (101-1)d\) | M1 | Ft on c's answer for \(d\). NMS/rep. addn., give both marks for '751'. SC if M0, award B1 for \(7n+44\) OE |
| \(\ldots = 51 + 100(7) = 751\) | A1F | Total: 2 |
| Answer | Marks | Guidance |
|---|---|---|
| Working | Mark | Guidance |
| \(S_n = \frac{100}{2}[751+1444]\) or \(S_n = \frac{100}{2}[2\times751+(100-1)7]\) | M1 | Formula for \(\{S_n\}\) with [any 3 of \(a=\) c's 751 (condoning '751'\(\pm d\)) or \(d=\) c's 7 or \(n=100\) or \(l=1444\) substituted] or \([S_{200}-S_k\) with \(k=100\), (condoning \(k=99\) or 101) stated/used with correct ft substitution in \(S_{200}\) or \(S_k\)] |
| \(= 109\,750\) | A1 | Total: 2 |
## Question 2:
### Part (a)
| Working | Mark | Guidance |
|---------|------|----------|
| $(d) = 7$ | B1 | 7 — **Total: 1** |
### Part (b)
| Working | Mark | Guidance |
|---------|------|----------|
| $(101^\text{st}\text{ term}) = a + (101-1)d$ | M1 | Ft on c's answer for $d$. NMS/rep. addn., give both marks for '751'. **SC** if M0, award B1 for $7n+44$ OE |
| $\ldots = 51 + 100(7) = 751$ | A1F | **Total: 2** |
### Part (c)
| Working | Mark | Guidance |
|---------|------|----------|
| $S_n = \frac{100}{2}[751+1444]$ **or** $S_n = \frac{100}{2}[2\times751+(100-1)7]$ | M1 | Formula for $\{S_n\}$ with [any **3** of $a=$ c's 751 (condoning '751'$\pm d$) **or** $d=$ c's 7 **or** $n=100$ **or** $l=1444$ substituted] or $[S_{200}-S_k$ with $k=100$, (condoning $k=99$ or 101) stated/used with correct ft substitution in $S_{200}$ or $S_k$] |
| $= 109\,750$ | A1 | **Total: 2** |
---2 The arithmetic series
$$51 + 58 + 65 + 72 + \ldots + 1444$$
has 200 terms.
\begin{enumerate}[label=(\alph*)]
\item Write down the common difference of the series.
\item Find the 101st term of the series.
\item Find the sum of the last 100 terms of the series.
\end{enumerate}
\hfill \mbox{\textit{AQA C2 2008 Q2 [5]}}