| Exam Board | Edexcel |
|---|---|
| Module | C1 (Core Mathematics 1) |
| Marks | 4 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Arithmetic Sequences and Series |
| Type | Recurrence relation: evaluate sum |
| Difficulty | Easy -1.2 This is a straightforward arithmetic sequence question from C1. Part (a) requires simple substitution into a recurrence relation (trivial). Part (b) involves recognizing it's an arithmetic series and applying the standard sum formula S_n = n/2(2a + (n-1)d), which is direct recall with minimal calculation. No problem-solving or insight required beyond standard textbook application. |
| Spec | 1.04e Sequences: nth term and recurrence relations1.04h Arithmetic sequences: nth term and sum formulae |
| Answer | Marks |
|---|---|
| (a) \(50, 48, 46, 44\) | B1 |
| (b) AP: \(a = 50, d = -2\) | B1 |
| \(S_{20} = \frac{20}{2}[100 + (19 \times -2)]\) | M1 |
| \(= 10 \times 62 = 620\) | A1 |
**(a)** $50, 48, 46, 44$ | B1 |
**(b)** AP: $a = 50, d = -2$ | B1 |
$S_{20} = \frac{20}{2}[100 + (19 \times -2)]$ | M1 |
$= 10 \times 62 = 620$ | A1 |
**Total: 4 marks**
---A sequence is defined by the recurrence relation
$$u_{n+1} = u_n - 2, \quad n > 0, \quad u_1 = 50.$$
\begin{enumerate}[label=(\alph*)]
\item Write down the first four terms of the sequence. [1]
\item Evaluate
$$\sum_{r=1}^{20} u_r.$$ [3]
\end{enumerate}
\hfill \mbox{\textit{Edexcel C1 Q3 [4]}}