| Exam Board | Edexcel |
|---|---|
| Module | C1 (Core Mathematics 1) |
| Session | Specimen |
| Marks | 9 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Arithmetic Sequences and Series |
| Type | Two related arithmetic progressions |
| Difficulty | Moderate -0.8 This is a straightforward application of arithmetic sequence formulas (nth term and sum) with clear structure and standard methods. Part (a) requires finding the 11th term, part (b) uses the sum formula directly, and part (c) involves setting two sums equal and solving—all routine C1 procedures with no conceptual challenges or novel problem-solving required. |
| Spec | 1.04h Arithmetic sequences: nth term and sum formulae |
| Answer | Marks | Guidance |
|---|---|---|
| \(a + (n-1)d = 250 + (10 \times 50) = £750\) | M1 A1 | (2 marks) |
| Answer | Marks | Guidance |
|---|---|---|
| \(\frac{1}{2}n[2a + (n-1)d] = \frac{1}{2} \times 20 \times (500 + 19 \times 50) = £14500\) | M1 A1, A1 | (3 marks) |
| Answer | Marks | Guidance |
|---|---|---|
| \(B: \frac{1}{2} \times 20 \times (24 + 19 \times 60) = [10(24 + 1140)] = \text{"14500"}\) | B1, M1 | |
| Solve for \(A\): \(A = 155\) | M1 A1 | (4 marks) |
## Part (a)
$a + (n-1)d = 250 + (10 \times 50) = £750$ | M1 A1 | (2 marks)
## Part (b)
$\frac{1}{2}n[2a + (n-1)d] = \frac{1}{2} \times 20 \times (500 + 19 \times 50) = £14500$ | M1 A1, A1 | (3 marks)
## Part (c)
$B: \frac{1}{2} \times 20 \times (24 + 19 \times 60) = [10(24 + 1140)] = \text{"14500"}$ | B1, M1 |
Solve for $A$: $A = 155$ | M1 A1 | (4 marks)
**Total: 9 marks**
---Ahmed plans to save £250 in the year 2001, £300 in 2002, £350 in 2003, and so on until the year 2020. His planned savings form an arithmetic sequence with common difference £50.
\begin{enumerate}[label=(\alph*)]
\item Find the amount he plans to save in the year 2011. [2]
\item Calculate his total planned savings over the 20 year period from 2001 to 2020. [3]
\end{enumerate}
Ben also plans to save money over the same 20 year period. He saves £$A$ in the year 2001 and his planned yearly savings form an arithmetic sequence with common difference £60.
Given that Ben's total planned savings over the 20 year period are equal to Ahmed's total planned savings over the same period,
\begin{enumerate}[label=(\alph*)]
\setcounter{enumi}{2}
\item calculate the value of $A$. [4]
\end{enumerate}
\hfill \mbox{\textit{Edexcel C1 Q7 [9]}}