| Exam Board | Edexcel |
|---|---|
| Module | F1 (Further Pure Mathematics 1) |
| Year | 2024 |
| Session | June |
| Marks | 8 |
| Paper | Download PDF ↗ |
| Topic | Sequences and series, recurrence and convergence |
| Type | Finding n for given sum value |
| Difficulty | Standard +0.3 This is a straightforward Further Maths summation question requiring standard formulas (∑r², ∑r, ∑r³) and algebraic manipulation. Part (a) is routine application of formulas, part (b) requires substitution and solving a cubic equation that likely factors nicely. While it's Further Maths content, it's a standard textbook exercise with no novel insight required, making it slightly easier than average overall. |
| Spec | 4.06a Summation formulae: sum of r, r^2, r^3 |
\begin{enumerate}
\item In this question use the standard results for summations.\\
(a) Show that for all positive integers $n$
\end{enumerate}
$$\sum _ { r = 1 } ^ { n } \left( 12 r ^ { 2 } + 2 r - 3 \right) = A n ^ { 3 } + B n ^ { 2 }$$
where $A$ and $B$ are integers to be determined.\\
(b) Hence determine the value of $n$ for which
$$\sum _ { r = 1 } ^ { 2 n } r ^ { 3 } - \sum _ { r = 1 } ^ { n } \left( 12 r ^ { 2 } + 2 r - 3 \right) = 270$$
\hfill \mbox{\textit{Edexcel F1 2024 Q7 [8]}}