| Exam Board | Edexcel |
|---|---|
| Module | C1 (Core Mathematics 1) |
| Year | 2008 |
| Session | June |
| Marks | 10 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Arithmetic Sequences and Series |
| Type | Real-world AP: find term or total |
| Difficulty | Easy -1.2 This is a straightforward arithmetic sequence question requiring only direct application of standard formulas (nth term and sum). Part (a) is simple verification, parts (b-c) use basic AP formulas with minimal algebraic manipulation, and parts (d-e) involve simple equation solving. No problem-solving insight or novel approaches needed—purely routine procedural work below typical A-level standard. |
| Spec | 1.04h Arithmetic sequences: nth term and sum formulae1.04i Geometric sequences: nth term and finite series sum |
| Answer | Marks | Guidance |
|---|---|---|
| Answer/Working | Marks | Guidance |
| \(5,7,9,11\) or \(5+2+2+2=11\) or \(5+6=11\); \(a=5\), \(d=2\), \(n=4\), \(t_4=11\) | B1 | Any other sum must have convincing argument |
| Answer | Marks | Guidance |
|---|---|---|
| Answer/Working | Marks | Guidance |
| \(t_n = a+(n-1)d\) with \(a=5\) or \(d=2\) correct | M1 | Other can be a letter; allow form \(2n+p\) \((p\neq5)\) |
| \(=5+2(n-1)\) or \(2n+3\) or \(1+2(n+1)\) | A1 | Must be in \(n\) not \(x\); correct answers with no working score 2/2 |
| Answer | Marks | Guidance |
|---|---|---|
| Answer/Working | Marks | Guidance |
| \(S_n=\frac{n}{2}[2\times5+2(n-1)]\) or \(\frac{n}{2}(5+\text{"their }2n+3\text{"})\) | M1A1 | |
| \(=\{n(5+n-1)\}=n(n+4)\) | A1cso | No incorrect working; must see \(S_n\) used |
| Answer | Marks | Guidance |
|---|---|---|
| Answer/Working | Marks | Guidance |
| \(43=2n+3\) | M1 | Form suitable equation in \(n\), attempt to solve |
| \([n]=20\) | A1 | Correct answer only scores 2/2 |
| Answer | Marks | Guidance |
|---|---|---|
| Answer/Working | Marks | Guidance |
| \(S_{20}=20\times24=\underline{480}\) (km) | M1A1 | \(n\) must be a value; accept 480 000 m etc. |
## Question 7:
### Part (a):
| Answer/Working | Marks | Guidance |
|---|---|---|
| $5,7,9,11$ or $5+2+2+2=11$ or $5+6=11$; $a=5$, $d=2$, $n=4$, $t_4=11$ | B1 | Any other sum must have convincing argument |
### Part (b):
| Answer/Working | Marks | Guidance |
|---|---|---|
| $t_n = a+(n-1)d$ with $a=5$ or $d=2$ correct | M1 | Other can be a letter; allow form $2n+p$ $(p\neq5)$ |
| $=5+2(n-1)$ or $2n+3$ or $1+2(n+1)$ | A1 | Must be in $n$ not $x$; correct answers with no working score 2/2 |
### Part (c):
| Answer/Working | Marks | Guidance |
|---|---|---|
| $S_n=\frac{n}{2}[2\times5+2(n-1)]$ or $\frac{n}{2}(5+\text{"their }2n+3\text{"})$ | M1A1 | |
| $=\{n(5+n-1)\}=n(n+4)$ | A1cso | No incorrect working; must see $S_n$ used |
### Part (d):
| Answer/Working | Marks | Guidance |
|---|---|---|
| $43=2n+3$ | M1 | Form suitable equation in $n$, attempt to solve |
| $[n]=20$ | A1 | Correct answer only scores 2/2 |
### Part (e):
| Answer/Working | Marks | Guidance |
|---|---|---|
| $S_{20}=20\times24=\underline{480}$ (km) | M1A1 | $n$ must be a value; accept 480 000 m etc. |
---7. Sue is training for a marathon. Her training includes a run every Saturday starting with a run of 5 km on the first Saturday. Each Saturday she increases the length of her run from the previous Saturday by 2 km .
\begin{enumerate}[label=(\alph*)]
\item Show that on the 4th Saturday of training she runs 11 km .
\item Find an expression, in terms of $n$, for the length of her training run on the $n$th Saturday.
\item Show that the total distance she runs on Saturdays in $n$ weeks of training is $n ( n + 4 ) \mathrm { km }$.
On the $n$th Saturday Sue runs 43 km .
\item Find the value of $n$.
\item Find the total distance, in km , Sue runs on Saturdays in $n$ weeks of training.
\end{enumerate}
\hfill \mbox{\textit{Edexcel C1 2008 Q7 [10]}}