| Exam Board | AQA |
|---|---|
| Module | FP1 (Further Pure Mathematics 1) |
| Year | 2014 |
| Session | June |
| Marks | 4 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Sequences and series, recurrence and convergence |
| Type | Standard summation formulae application |
| Difficulty | Standard +0.3 This is a straightforward algebraic manipulation question requiring expansion of r²(r-6) into r³-6r², then applying standard summation formulae with adjusted limits. The technique of splitting sums and adjusting indices is routine for FP1, though slightly above average difficulty due to the non-standard starting index requiring careful arithmetic. |
| Spec | 4.06a Summation formulae: sum of r, r^2, r^3 |
Use the formulae for $\sum_{r=1}^{n} r^3$ and $\sum_{r=1}^{n} r^2$ to find the value of
$$\sum_{r=3}^{60} r^2(r - 6)$$
[4 marks]
\hfill \mbox{\textit{AQA FP1 2014 Q3 [4]}}