| Exam Board | Edexcel |
|---|---|
| Module | C1 (Core Mathematics 1) |
| Marks | 7 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Arithmetic Sequences and Series |
| Type | Sigma notation: arithmetic series evaluation |
| Difficulty | Moderate -0.8 This is a straightforward C1 arithmetic series question requiring standard formula application. Part (a) involves recognizing an arithmetic sequence and applying the sum formula with clear first/last terms. Part (b) requires algebraic manipulation to separate the sum into standard results (Σr and Σ1), then factorizing to match the given form—routine techniques with no conceptual challenges or novel problem-solving required. |
| Spec | 1.04g Sigma notation: for sums of series1.04h Arithmetic sequences: nth term and sum formulae |
| Answer | Marks | Guidance |
|---|---|---|
| (a) AP: \(a = 77, l = -70\) | B1 | |
| \(S_{50} = \frac{50}{2}[77 + (-70)] = 25 \times 7 = 175\) | M1 A1 | |
| (b) AP: \(a = 2, d = \frac{1}{4}\) | B2 | |
| \(S_n = \frac{n}{2}[4 + \frac{1}{4}(n-1)]\) | M1 | |
| \(= \frac{1}{4}n[8 + (n-1)] = \frac{1}{4}n(n + 7)\) | A1 | \([k = \frac{1}{4}]\) |
**(a)** AP: $a = 77, l = -70$ | B1 |
$S_{50} = \frac{50}{2}[77 + (-70)] = 25 \times 7 = 175$ | M1 A1 |
**(b)** AP: $a = 2, d = \frac{1}{4}$ | B2 |
$S_n = \frac{n}{2}[4 + \frac{1}{4}(n-1)]$ | M1 |
$= \frac{1}{4}n[8 + (n-1)] = \frac{1}{4}n(n + 7)$ | A1 | $[k = \frac{1}{4}]$ | (7)\begin{enumerate}[label=(\alph*)]
\item Evaluate
$$\sum_{r=1}^{50} (80 - 3r).$$ [3]
\item Show that
$$\sum_{r=1}^{n} \frac{r + 3}{2} = k n(n + 7),$$
where $k$ is a rational constant to be found. [4]
\end{enumerate}
\hfill \mbox{\textit{Edexcel C1 Q6 [7]}}