| Exam Board | Edexcel |
|---|---|
| Module | C1 (Core Mathematics 1) |
| Year | 2008 |
| Session | January |
| Marks | 7 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Arithmetic Sequences and Series |
| Type | Largest or extreme value of sum |
| Difficulty | Standard +0.3 This is a straightforward arithmetic sequence problem requiring standard formulas (nth term, finding n when term equals zero, and sum formula). Part (c) requires recognizing that the sum is maximized when terms become negative, but this is a direct application once parts (a) and (b) are solved. Slightly above average difficulty due to the multi-step nature and the optimization aspect, but all techniques are routine for C1. |
| Spec | 1.04h Arithmetic sequences: nth term and sum formulae |
| Answer | Marks |
|---|---|
| (a) \(u_{25} = a + 24d = 30 + 24 \times (-1.5)\) | M1 |
| \(= -6\) | A1 |
| Answer | Marks |
|---|---|
| (b) \(a + (n-1)d = 30 - 1.5(r-1) = 0\) | M1 |
| \(r = 21\) | A1 |
| Answer | Marks |
|---|---|
| (c) \(S_{20} = \frac{20}{2}\{60 + 19(-1.5)\}\) or \(S_{21} = \frac{21}{2}\{60 + 20(-1.5)\}\) or \(S_{21} = \frac{21}{2}\{30 + 0\}\) | M1, A1ft |
| \(= 315\) | A1 |
(a) $u_{25} = a + 24d = 30 + 24 \times (-1.5)$ | M1 |
$= -6$ | A1 |
**Total for (a): 2 marks**
(b) $a + (n-1)d = 30 - 1.5(r-1) = 0$ | M1 |
$r = 21$ | A1 |
**Total for (b): 2 marks**
(c) $S_{20} = \frac{20}{2}\{60 + 19(-1.5)\}$ or $S_{21} = \frac{21}{2}\{60 + 20(-1.5)\}$ or $S_{21} = \frac{21}{2}\{30 + 0\}$ | M1, A1ft |
$= 315$ | A1 |
**Total for (c): 3 marks**
**Total: 7 marks**11. The first term of an arithmetic sequence is 30 and the common difference is - 1.5
\begin{enumerate}[label=(\alph*)]
\item Find the value of the 25th term.
The $r$ th term of the sequence is 0 .
\item Find the value of $r$.
The sum of the first $n$ terms of the sequence is $S _ { n }$.
\item Find the largest positive value of $S _ { n }$.
\end{enumerate}
\hfill \mbox{\textit{Edexcel C1 2008 Q11 [7]}}