| Exam Board | OCR |
|---|---|
| Module | C2 (Core Mathematics 2) |
| Marks | 7 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Arithmetic Sequences and Series |
| Type | Sigma notation: arithmetic series evaluation |
| Difficulty | Moderate -0.8 Part (i) is a straightforward application of the arithmetic series formula to evaluate a sum in sigma notation—pure recall and substitution. Part (ii) requires simplifying the summand, splitting into standard sums, and algebraic manipulation to match the given form, but follows a standard template for C2. Both parts are routine exercises with no novel problem-solving required, making this easier than average. |
| Spec | 1.04g Sigma notation: for sums of series1.04h Arithmetic sequences: nth term and sum formulae |
\begin{enumerate}
\item (i) Evaluate
\end{enumerate}
$$\sum _ { r = 1 } ^ { 50 } ( 80 - 3 r )$$
(ii) Show that
$$\sum _ { r = 1 } ^ { n } \frac { r + 3 } { 2 } = k n ( n + 7 )$$
where $k$ is a rational constant to be found.\\
\hfill \mbox{\textit{OCR C2 Q3 [7]}}