| Exam Board | OCR |
|---|---|
| Module | H240/01 (Pure Mathematics) |
| Marks | 10 |
| Paper | Download PDF ↗ |
| Topic | Arithmetic Sequences and Series |
| Type | Real-world AP: find n satisfying a condition |
| Difficulty | Moderate -0.8 This is a straightforward application of standard arithmetic and geometric series formulas to a real-world context. Parts (a)-(c) require direct substitution into well-known formulas (S_n = n/2(2a + (n-1)d) and S_n = a(1-r^n)/(1-r)), with part (c) involving solving a quadratic equation. Part (d) requires basic understanding of series convergence. No novel problem-solving or insight needed—purely routine application of AS-level series content. |
| 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 |
7 Business A made a $\pounds 5000$ profit during its first year.\\
In each subsequent year, the profit increased by $\pounds 1500$ so that the profit was $\pounds 6500$ during the second year, $\pounds 8000$ during the third year and so on.
Business B made a $\pounds 5000$ 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.
\item Find an expression for the total profit made by business B during the first $n$ years.
Give your answer in its simplest form.
\item Find how many years it will take for the total profit of business A to reach $\pounds 385000$.
\item Comment on the profits made by each business in the long term.
\end{enumerate}
\hfill \mbox{\textit{OCR H240/01 Q7 [10]}}