| Exam Board | Edexcel |
|---|---|
| Module | C1 (Core Mathematics 1) |
| Marks | 6 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Arithmetic Sequences and Series |
| Type | Sigma notation: arithmetic series evaluation |
| Difficulty | Easy -1.2 This is a straightforward C1 question testing basic understanding of sigma notation and arithmetic series. Part (a) requires simple substitution (r=1, r=2), part (b) is immediate from the result, and part (c) applies a standard formula. No problem-solving or insight needed—pure routine application of basic techniques. |
| Spec | 1.04h Arithmetic sequences: nth term and sum formulae |
| Answer | Marks | Guidance |
|---|---|---|
| First term (\(r=1\)): \(80-3(1) = 77\); Second term (\(r=2\)): \(80-3(2) = 74\) | B1 B1 | B1 each term |
| Answer | Marks |
|---|---|
| Common difference \(d = -3\) | B1 |
| Answer | Marks | Guidance |
|---|---|---|
| \(S_{50} = \frac{50}{2}(2(77) + 49(-3))\) or \(\frac{50}{2}(77+(-70))\) | M1 A1 | M1 for use of correct sum formula |
| \(= 25(154-147) = 25 \times 7 = 175\) | A1 |
# Question 2:
## Part (a):
| First term ($r=1$): $80-3(1) = 77$; Second term ($r=2$): $80-3(2) = 74$ | B1 B1 | B1 each term |
## Part (b):
| Common difference $d = -3$ | B1 | |
## Part (c):
| $S_{50} = \frac{50}{2}(2(77) + 49(-3))$ or $\frac{50}{2}(77+(-70))$ | M1 A1 | M1 for use of correct sum formula |
| $= 25(154-147) = 25 \times 7 = 175$ | A1 | |
---2. The sum of an arithmetic series is
$$\sum _ { r = 1 } ^ { n } ( 80 - 3 r ) .$$
\begin{enumerate}[label=(\alph*)]
\item Write down the first two terms of the series.
\item Find the common difference of the series.
Given that $n = 50$,
\item find the sum of the series.
\end{enumerate}
\hfill \mbox{\textit{Edexcel C1 Q2 [6]}}