| Exam Board | Edexcel |
|---|---|
| Module | C1 (Core Mathematics 1) |
| Marks | 10 |
| Paper | Download PDF ↗ |
| Topic | Arithmetic Sequences and Series |
| Type | Prove sum formula |
| Difficulty | Moderate -0.8 This is a straightforward C1 arithmetic series question requiring standard formula derivation (bookwork proof) and routine application to a context. Part (a) is a standard proof, part (b) involves substituting into the sum formula and solving a linear equation, and part (c) requires finding a single term. All steps are mechanical with no problem-solving insight needed, making it easier than average. |
| Spec | 1.01a Proof: structure of mathematical proof and logical steps1.04h Arithmetic sequences: nth term and sum formulae |
\begin{enumerate}[label=(\alph*)]
\item An arithmetic series has first term $a$ and common difference $d$. Prove that the sum of the first $n$ terms of the series is
$$\frac{1}{2}n[2a + (n-1)d].$$ [4]
\end{enumerate}
A company made a profit of £54 000 in the year 2001. A model for future performance assumes that yearly profits will increase in an arithmetic sequence with common difference £$d$. This model predicts total profits of £619 200 for the 9 years 2001 to 2009 inclusive.
\begin{enumerate}[label=(\alph*)]
\setcounter{enumi}{1}
\item Find the value of $d$. [4]
\end{enumerate}
Using your value of $d$,
\begin{enumerate}[label=(\alph*)]
\setcounter{enumi}{2}
\item find the predicted profit for the year 2011. [2]
\end{enumerate}
\hfill \mbox{\textit{Edexcel C1 Q18 [10]}}