| Exam Board | Edexcel |
|---|---|
| Module | F1 (Further Pure Mathematics 1) |
| Year | 2023 |
| Session | January |
| Marks | 6 |
| Paper | Download PDF ↗ |
| Topic | Sequences and series, recurrence and convergence |
| Type | Finding constants from given sum formula |
| Difficulty | Standard +0.3 This is a straightforward Further Maths question requiring expansion of (7r-5)², application of standard summation formulas, algebraic simplification, and factorization to match the given form. While it involves multiple steps and careful algebra, it follows a completely standard template with no novel insight required—students practicing F1 will have seen many similar problems. |
| Spec | 1.04g Sigma notation: for sums of series4.06a Summation formulae: sum of r, r^2, r^3 |
\begin{enumerate}
\item In this question you must show all stages of your working. Solutions relying entirely on calculator technology are not acceptable.
\end{enumerate}
Use the standard results for $\sum _ { r = 1 } ^ { n } r$ and $\sum _ { r = 1 } ^ { n } r ^ { 2 }$ to show that for all positive integers $n$
$$\sum _ { r = 1 } ^ { n } ( 7 r - 5 ) ^ { 2 } = \frac { n } { 6 } ( 7 n + 1 ) ( A n + B )$$
where $A$ and $B$ are integers to be determined.
\hfill \mbox{\textit{Edexcel F1 2023 Q2 [6]}}