| Exam Board | Edexcel |
|---|---|
| Module | C1 (Core Mathematics 1) |
| Marks | 8 |
| Paper | Download PDF ↗ |
| Topic | Arithmetic Sequences and Series |
| Type | Two related arithmetic progressions |
| Difficulty | Moderate -0.8 This is a straightforward arithmetic sequence question requiring only standard formulas for nth term and sum. Part (a) uses a = 500, d = 50, n = 40 directly. Part (b) applies the sum formula. Part (c) involves equating two sums and solving for d. All steps are routine applications of memorized formulas with no problem-solving insight required, making it easier than average but not trivial due to the multi-part structure. |
| Spec | 1.04h Arithmetic sequences: nth term and sum formulae |
Each year, for 40 years, Anne will pay money into a savings scheme. In the first year she pays £500. Her payments then increase by £50 each year, so that she pays £550 in the second year, £600 in the third year, and so on.
\begin{enumerate}[label=(\alph*)]
\item Find the amount that Anne will pay in the 40th year. [2]
\item Find the total amount that Anne will pay in over the 40 years. [2]
\end{enumerate}
Over the same 40 years, Brian will also pay money into the savings scheme. In the first year he pays in £890 and his payments then increase by £$d$ each year.
Given that Brian and Anne will pay in exactly the same amount over the 40 years,
\begin{enumerate}[label=(\alph*)]
\setcounter{enumi}{2}
\item find the value of $d$. [4]
\end{enumerate}
\hfill \mbox{\textit{Edexcel C1 Q7 [8]}}