| Exam Board | Edexcel |
|---|---|
| Module | C1 (Core Mathematics 1) |
| Marks | 8 |
| Paper | Download PDF ↗ |
| Topic | Arithmetic Sequences and Series |
| Type | Real-world AP: find term or total |
| Difficulty | Moderate -0.8 This is a straightforward arithmetic sequence question requiring direct application of standard formulas. Part (a) involves simple substitution into nth term and sum formulas with given values. Part (b) requires solving a quadratic inequality, which is routine for C1 level. All steps are mechanical with no problem-solving insight needed. |
| Spec | 1.04h Arithmetic sequences: nth term and sum formulae |
In the first month after opening, a mobile phone shop sold 280 phones. A model for future trading assumes that sales will increase by $x$ phones per month for the next 35 months, so that $(280 + x)$ phones will be sold in the second month, $(280 + 2x)$ in the third month, and so on.
Using this model with $x = 5$, calculate
\begin{enumerate}[label=(\alph*)]
\item
\begin{enumerate}[label=(\roman*)]
\item the number of phones sold in the 36th month, [2]
\item the total number of phones sold over the 36 months. [2]
\end{enumerate}
\end{enumerate}
The shop sets a sales target of 17 000 phones to be sold over the 36 months.
Using the same model,
\begin{enumerate}[label=(\alph*)]
\setcounter{enumi}{1}
\item find the least value of $x$ required to achieve this target. [4]
\end{enumerate}
\hfill \mbox{\textit{Edexcel C1 Q26 [8]}}