Edexcel C1 — Question 34 8 marks

Exam BoardEdexcel
ModuleC1 (Core Mathematics 1)
Marks8
PaperDownload PDF ↗
TopicArithmetic Sequences and Series
TypeArithmetic progression with parameters
DifficultyStandard +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.
Spec1.01a 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.
  1. Show that \(p = 4\). [2]
  2. Find the value of the 40th term of this series. [3]
  3. Prove that the sum of the first \(n\) terms of the series is a perfect square. [3]

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]}}