| Exam Board | Edexcel |
|---|---|
| Module | F1 (Further Pure Mathematics 1) |
| Year | 2015 |
| Session | June |
| Marks | 5 |
| 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 application of standard summation formulas. Students expand (3r-2)², split into separate sums, apply the given formulas for Σr and Σr², then simplify to match the required form. It's mechanical algebra with no problem-solving insight required, making it slightly easier than average despite being Further Maths content. |
| Spec | 4.06a Summation formulae: sum of r, r^2, r^3 |
\begin{enumerate}
\item Use the standard results for $\sum _ { r = 1 } ^ { n } r$ and for $\sum _ { r = 1 } ^ { n } r ^ { 2 }$ to show that
\end{enumerate}
$$\sum _ { r = 1 } ^ { n } ( 3 r - 2 ) ^ { 2 } = \frac { n } { 2 } \left( a n ^ { 2 } + b n + c \right)$$
where $a , b$ and $c$ are integers to be found.\\
\hfill \mbox{\textit{Edexcel F1 2015 Q2 [5]}}