OCR C2 — Question 3 7 marks

Exam BoardOCR
ModuleC2 (Core Mathematics 2)
Marks7
PaperDownload PDF ↗
Mark schemeDownload PDF ↗
TopicArithmetic Sequences and Series
TypeSigma notation: arithmetic series evaluation
DifficultyModerate -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.
Spec1.04g Sigma notation: for sums of series1.04h Arithmetic sequences: nth term and sum formulae

  1. (i) Evaluate
$$\sum _ { r = 1 } ^ { 50 } ( 80 - 3 r )$$ (ii) Show that $$\sum _ { r = 1 } ^ { n } \frac { r + 3 } { 2 } = k n ( n + 7 )$$ where \(k\) is a rational constant to be found.

\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]}}