| Exam Board | SPS |
|---|---|
| Module | SPS FM Pure (SPS FM Pure) |
| Year | 2021 |
| Session | May |
| Marks | 3 |
| Topic | Sequences and series, recurrence and convergence |
| Type | Standard summation formulae application |
| Difficulty | Easy -1.2 This is a straightforward algebraic manipulation question requiring expansion of r(3r-2) into 3r² - 2r, then applying two standard summation formulae and arithmetic. It's purely procedural with no problem-solving or insight needed, making it easier than average, though not trivial since it requires correct formula application. |
| Spec | 4.06a Summation formulae: sum of r, r^2, r^3 |
Using the formulae for $\sum_{r=1}^{n} r$ and $\sum_{r=1}^{n} r^2$, show that $\sum_{r=1}^{10} r(3r - 2) = 1045$. [3]
\hfill \mbox{\textit{SPS SPS FM Pure 2021 Q4 [3]}}