Edexcel FP1 — Question 2 7 marks

Exam BoardEdexcel
ModuleFP1 (Further Pure Mathematics 1)
Marks7
PaperDownload PDF ↗
TopicSequences and series, recurrence and convergence
TypeStandard summation formulae application
DifficultyModerate -0.3 Part (a) is a straightforward application of standard summation formulae requiring algebraic manipulation to verify a given result—routine for FP1 students. Part (b) appears to have a typo (likely asking for a specific n or different sum), but even interpreting generously, this is a standard textbook exercise testing formula recall and algebraic verification rather than problem-solving or novel insight.
Spec4.06a Summation formulae: sum of r, r^2, r^3

  1. Show, using the formulae for \(\sum r\) and \(\sum r^2\), that $$\sum_{r=1}^n (6r^2 + 4r - 1) = n(n + 2)(2n + 1).$$ [5]
  2. Hence, or otherwise, find the value of \(\sum_{r=1}^n (6r^2 + 4r - 1)\). [2]

\begin{enumerate}[label=(\alph*)]
\item Show, using the formulae for $\sum r$ and $\sum r^2$, that
$$\sum_{r=1}^n (6r^2 + 4r - 1) = n(n + 2)(2n + 1).$$
[5]

\item Hence, or otherwise, find the value of $\sum_{r=1}^n (6r^2 + 4r - 1)$.
[2]
\end{enumerate}

\hfill \mbox{\textit{Edexcel FP1  Q2 [7]}}