| Exam Board | Edexcel |
|---|---|
| Module | C1 (Core Mathematics 1) |
| Marks | 10 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Arithmetic Sequences and Series |
| Type | Real-world AP: find term or total |
| Difficulty | Moderate -0.8 This is a straightforward arithmetic series question requiring only standard formula application. Part (a) uses the sum formula with known values, (b) is direct substitution, (c) involves algebraic manipulation of the sum formula, and (d) requires basic interpretation. All techniques are routine C1 level with no problem-solving insight needed. |
| Spec | 1.02z Models in context: use functions in modelling1.04h Arithmetic sequences: nth term and sum formulae |
| Answer | Marks | Guidance |
|---|---|---|
| (a) | \(S_n = \frac{n}{2}[3000 + (5 - x)] = 8100\) | M1 A1 |
| \(3000 - 5x = 2700,\) \(x = 60\) | M1 A1 | |
| (b) | \(= 1500 - (7 \times 60) = 1500 - 420 = £1080\) | M1 A1 |
| (c) | \(S_n = \frac{n}{2}[3000 - 60(n-1)]\) | M1 |
| \(= n[1500 - 30(n-1)]\) | M1 A1 | |
| \(= 30n[50 - (n-1)] = 30n(51 - n)\) | \([k = 30]\) | M1 A1 |
| (d) | the value of sales in a month would become negative which is not possible | B1 |
(a) | $S_n = \frac{n}{2}[3000 + (5 - x)] = 8100$ | M1 A1 |
| $3000 - 5x = 2700,$ $x = 60$ | M1 A1 |
(b) | $= 1500 - (7 \times 60) = 1500 - 420 = £1080$ | M1 A1 |
(c) | $S_n = \frac{n}{2}[3000 - 60(n-1)]$ | M1 |
| $= n[1500 - 30(n-1)]$ | M1 A1 |
| $= 30n[50 - (n-1)] = 30n(51 - n)$ | $[k = 30]$ | M1 A1 |
(d) | the value of sales in a month would become negative which is not possible | B1 | (10)A store begins to stock a new range of DVD players and achieves sales of £1500 of these products during the first month.
In a model it is assumed that sales will decrease by £$x$ in each subsequent month, so that sales of £$(1500 - x)$ and £$(1500 - 2x)$ will be achieved in the second and third months respectively.
Given that sales total £8100 during the first six months, use the model to
\begin{enumerate}[label=(\alph*)]
\item find the value of $x$, [4]
\item find the expected value of sales in the eighth month, [2]
\item show that the expected total of sales in pounds during the first $n$ months is given by $kn(51 - n)$, where $k$ is an integer to be found. [3]
\item Explain why this model cannot be valid over a long period of time. [1]
\end{enumerate}
\hfill \mbox{\textit{Edexcel C1 Q9 [10]}}