| Exam Board | Edexcel |
|---|---|
| Module | C1 (Core Mathematics 1) |
| Year | 2011 |
| Session | January |
| Marks | 7 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Arithmetic Sequences and Series |
| Type | Arithmetic progression with parameters |
| Difficulty | Moderate -0.8 This is a straightforward application of standard arithmetic sequence formulas (S_n and nth term). Part (a) is a 'show that' requiring direct substitution into the sum formula, while parts (b) and (c) involve forming and solving simultaneous linear equations—all routine procedures for C1 with no problem-solving insight required. |
| Spec | 1.04h Arithmetic sequences: nth term and sum formulae |
| Answer | Marks | Guidance |
|---|---|---|
| \(S_{10} = \dfrac{10}{2}[2a + 9d]\) or expansion giving \(162 = 10a + 45d\) | M1, A1cso | M1 for use of \(S_n\) with \(n=10\) |
| (2 marks total) |
| Answer | Marks | Guidance |
|---|---|---|
| \((u_n = a+(n-1)d \Rightarrow)\ 17 = a + 5d\) | B1 | |
| \(10 \times (b)\) gives \(10a + 50d = 170\); (a) is \(10a + 45d = 162\) | M1 | For attempt to eliminate \(a\) or \(d\) from their two linear equations |
| Subtract: \(5d = 8\), so \(d = \underline{1.6}\) o.e. | A1 | |
| Solving for \(a\): \(a = 17 - 5d\) | M1 | For using their value of \(a\) or \(d\) to find the other value |
| so \(a = \underline{9}\) | A1 | |
| (4 marks total) |
## Question 6:
### Part (a):
| $S_{10} = \dfrac{10}{2}[2a + 9d]$ or expansion giving $162 = 10a + 45d$ | M1, A1cso | M1 for use of $S_n$ with $n=10$ |
|(2 marks total)|||
### Part (b):
| $(u_n = a+(n-1)d \Rightarrow)\ 17 = a + 5d$ | B1 | |
| $10 \times (b)$ gives $10a + 50d = 170$; (a) is $10a + 45d = 162$ | M1 | For attempt to eliminate $a$ or $d$ from their two linear equations |
| Subtract: $5d = 8$, so $d = \underline{1.6}$ o.e. | A1 | |
| Solving for $a$: $a = 17 - 5d$ | M1 | For using their value of $a$ or $d$ to find the other value |
| so $a = \underline{9}$ | A1 | |
|(4 marks total)|||
---6. An arithmetic sequence has first term $a$ and common difference $d$. The sum of the first 10 terms of the sequence is 162 .
\begin{enumerate}[label=(\alph*)]
\item Show that $10 a + 45 d = 162$
Given also that the sixth term of the sequence is 17 ,
\item write down a second equation in $a$ and $d$,
\item find the value of $a$ and the value of $d$.
\end{enumerate}
\hfill \mbox{\textit{Edexcel C1 2011 Q6 [7]}}