| Exam Board | Edexcel |
|---|---|
| Module | C2 (Core Mathematics 2) |
| Marks | 13 |
| Paper | Download PDF ↗ |
| Topic | Arithmetic Sequences and Series |
| Type | Prove sum formula |
| Difficulty | Moderate -0.3 This is a standard C2 sequences and series question with routine applications. Part (a) is a bookwork proof of the arithmetic series formula (4 marks for a standard derivation). Parts (b)-(d) involve straightforward substitution into formulas: finding d from given sum, calculating a future term, and applying geometric sequence formula. All techniques are direct applications with no problem-solving insight required, making it slightly easier than average. |
| Spec | 1.04h 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}
An alternative model assumes that the company's yearly profits will increase in a geometric sequence with common ratio 1.06. Using this alternative model and again taking the profit in 2001 to be £54 000,
\begin{enumerate}[label=(\alph*)]
\setcounter{enumi}{3}
\item find the predicted profit for the year 2011. [3]
\end{enumerate}
\hfill \mbox{\textit{Edexcel C2 Q32 [13]}}