| Exam Board | OCR |
|---|---|
| Module | H240/01 (Pure Mathematics) |
| Year | 2017 |
| Session | Specimen |
| Marks | 10 |
| Topic | Arithmetic Sequences and Series |
| Type | Real-world AP: find n satisfying a condition |
| Difficulty | Moderate -0.8 This is a straightforward arithmetic and geometric series question with standard applications. Parts (a)-(c) involve direct formula application (sum of AP and GP), while part (d) requires basic understanding of series convergence. The calculations are routine with no conceptual challenges or novel problem-solving required. |
| Spec | 1.04h Arithmetic sequences: nth term and sum formulae1.04i Geometric sequences: nth term and finite series sum1.04j Sum to infinity: convergent geometric series |r|<1 |
Business A made a £5000 profit during its first year.
In each subsequent year, the profit increased by £1500 so that the profit was £6500 during the second year, £8000 during the third year and so on.
Business B made a £5000 profit during its first year.
In each subsequent year, the profit was 90% of the previous year's profit.
\begin{enumerate}[label=(\alph*)]
\item Find an expression for the total profit made by business A during the first $n$ years.
Give your answer in its simplest form. [2]
\item Find an expression for the total profit made by business B during the first $n$ years.
Give your answer in its simplest form. [3]
\item Find how many years it will take for the total profit of business A to reach £385 000. [3]
\item Comment on the profits made by each business in the long term. [2]
\end{enumerate}
\hfill \mbox{\textit{OCR H240/01 2017 Q7 [10]}}