| Exam Board | Edexcel |
|---|---|
| Module | C1 (Core Mathematics 1) |
| Marks | 8 |
| Paper | Download PDF ↗ |
| Topic | Arithmetic Sequences and Series |
| Type | Arithmetic progression with parameters |
| Difficulty | Standard +0.8 This C1 question requires understanding arithmetic sequences (standard), but part (c) demands algebraic manipulation to prove the sum is a perfect square, which requires insight beyond routine application. The multi-step proof element elevates it above typical C1 exercises (which average 0.0), though it remains accessible with systematic algebra. |
| Spec | 1.01a Proof: structure of mathematical proof and logical steps1.04h Arithmetic sequences: nth term and sum formulae |
The first three terms of an arithmetic series are $p$, $5p - 8$, and $3p + 8$ respectively.
\begin{enumerate}[label=(\alph*)]
\item Show that $p = 4$. [2]
\item Find the value of the 40th term of this series. [3]
\item Prove that the sum of the first $n$ terms of the series is a perfect square. [3]
\end{enumerate}
\hfill \mbox{\textit{Edexcel C1 Q34 [8]}}