| Exam Board | Edexcel |
|---|---|
| Module | C2 (Core Mathematics 2) |
| Marks | 9 |
| Paper | Download PDF ↗ |
| Topic | Geometric Sequences and Series |
| Type | Find year when threshold exceeded |
| Difficulty | Moderate -0.8 This is a straightforward application of geometric sequences requiring only standard formulas and basic logarithm manipulation. Part (a) is direct recall, part (b) is a routine 'show that' using logarithms, and parts (c)-(d) involve plugging values into standard formulas. The context is accessible and all steps are procedural with no novel insight required. |
| Spec | 1.04i Geometric sequences: nth term and finite series sum1.06f Laws of logarithms: addition, subtraction, power rules1.06g Equations with exponentials: solve a^x = b |
A trading company made a profit of £50 000 in 2006 (Year 1).
A model for future trading predicts that profits will increase year by year in a geometric sequence with common ratio $r, r > 1$.
The model therefore predicts that in 2007 (Year 2) a profit of £50 000r will be made.
\begin{enumerate}[label=(\alph*)]
\item Write down an expression for the predicted profit in Year $n$.
[1]
\end{enumerate}
The model predicts that in Year $n$, the profit made will exceed £200 000.
\begin{enumerate}[label=(\alph*)]
\setcounter{enumi}{1}
\item Show that $n > \frac{\log 4}{\log r} + 1$.
[3]
\end{enumerate}
Using the model with $r = 1.09$,
\begin{enumerate}[label=(\alph*)]
\setcounter{enumi}{2}
\item find the year in which the profit made will first exceed £200 000,
[2]
\item find the total of the profits that will be made by the company over the 10 years from 2006 to 2015 inclusive, giving your answer to the nearest £10 000.
[3]
\end{enumerate}
\hfill \mbox{\textit{Edexcel C2 Q8 [9]}}