| Exam Board | Edexcel |
|---|---|
| Module | C1 (Core Mathematics 1) |
| Marks | 10 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Arithmetic Sequences and Series |
| Type | Arithmetic progression with parameters |
| Difficulty | Moderate -0.3 This is a standard C1 arithmetic sequence question requiring routine application of the common difference formula, nth term formula, and sum formula. Part (a) involves solving a linear equation, parts (b-c) are direct formula applications, and part (d) requires solving an inequality—all standard techniques with no novel insight needed. Slightly easier than average due to straightforward algebraic manipulation. |
| Spec | 1.04h Arithmetic sequences: nth term and sum formulae1.04i Geometric sequences: nth term and finite series sum |
| Answer | Marks |
|---|---|
| (a) \(2p - (12 - p) = (4p - 5) - 2p\) | M1 |
| \(p = 7\) | A1 |
| (b) \(a = 12 - 7 = 5, a + d = 2 \times 7 = 14 \therefore d = 9\) | B1 |
| \(u_5 = 5 + (5 \times 9) = 5 + 45 = 50\) | M1 A1 |
| (c) \(= \frac{15}{2}[10 + (14 \times 9)] = \frac{15}{2} \times 136 = 1020\) | M1 A1 |
| (d) \(5 + 9(n - 1) < 400\) | M1 |
| \(n < \frac{395}{9} + 1\) | M1 |
| \(n < 44\frac{8}{9} \therefore 44\) terms | A1 |
**(a)** $2p - (12 - p) = (4p - 5) - 2p$ | M1 |
$p = 7$ | A1 |
**(b)** $a = 12 - 7 = 5, a + d = 2 \times 7 = 14 \therefore d = 9$ | B1 |
$u_5 = 5 + (5 \times 9) = 5 + 45 = 50$ | M1 A1 |
**(c)** $= \frac{15}{2}[10 + (14 \times 9)] = \frac{15}{2} \times 136 = 1020$ | M1 A1 |
**(d)** $5 + 9(n - 1) < 400$ | M1 |
$n < \frac{395}{9} + 1$ | M1 |
$n < 44\frac{8}{9} \therefore 44$ terms | A1 |
**Total: 10 marks**
---The first three terms of an arithmetic series are $(12 - p)$, $2p$ and $(4p - 5)$ respectively, where $p$ is a constant.
\begin{enumerate}[label=(\alph*)]
\item Find the value of $p$. [2]
\item Show that the sixth term of the series is 50. [3]
\item Find the sum of the first 15 terms of the series. [2]
\item Find how many terms of the series have a value of less than 400. [3]
\end{enumerate}
\hfill \mbox{\textit{Edexcel C1 Q7 [10]}}