| Exam Board | Edexcel |
|---|---|
| Module | C12 (Core Mathematics 1 & 2) |
| Year | 2014 |
| Session | January |
| Marks | 8 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Arithmetic Sequences and Series |
| Type | Arithmetic progression with parameters |
| Difficulty | Moderate -0.8 This is a straightforward arithmetic sequence question requiring only standard techniques: using the common difference property to find p, applying the nth term formula, and deriving the sum formula. All parts are routine applications of well-practiced formulas with no problem-solving insight needed, making it easier than average but not trivial due to the algebraic manipulation required. |
| Spec | 1.04g Sigma notation: for sums of series1.04h Arithmetic sequences: nth term and sum formulae |
| Answer | Marks | Guidance |
|---|---|---|
| Uses \((2p-6) - 4p = 4p - 60\) or \(4p = \frac{60+(2p-6)}{2}\) or two correct equations with \(d\); so \(p = 9\) | M1, A1* | Correct equation to enable \(p\) to be found or two correct simultaneous equations |
| Answer | Marks | Guidance |
|---|---|---|
| Uses \(a + 19d\) with \(a = 60\); finds \(d = 36 - 60 = -24\); obtains \(-396\) | M1, B1, A1 | \(d = -24\) seen in (a) or (b); need 20 terms for M1; cso |
| Answer | Marks | Guidance |
|---|---|---|
| Uses \(\frac{n}{2}(2 \times 60 + (n-1)d)\); uses \(\frac{n}{2}(2\times 60 - 24(n-1))\) | M1, A1 | Correct formula with their value of \(d\) |
| \(= 12n(6-n)\) | A1* | Given answer — must be no errors to award this mark |
## Question 11:
### Part (a):
| Uses $(2p-6) - 4p = 4p - 60$ or $4p = \frac{60+(2p-6)}{2}$ or two correct equations with $d$; so $p = 9$ | M1, A1* | Correct equation to enable $p$ to be found or two correct simultaneous equations |
### Part (b):
| Uses $a + 19d$ with $a = 60$; finds $d = 36 - 60 = -24$; obtains $-396$ | M1, B1, A1 | $d = -24$ seen in (a) or (b); need 20 terms for M1; cso |
### Part (c):
| Uses $\frac{n}{2}(2 \times 60 + (n-1)d)$; uses $\frac{n}{2}(2\times 60 - 24(n-1))$ | M1, A1 | Correct formula with their value of $d$ |
| $= 12n(6-n)$ | A1* | Given answer — must be no errors to award this mark |11. The first three terms of an arithmetic series are $60,4 p$ and $2 p - 6$ respectively.
\begin{enumerate}[label=(\alph*)]
\item Show that $p = 9$
\item Find the value of the 20th term of this series.
\item Prove that the sum of the first $n$ terms of this series is given by the expression
$$12 n ( 6 - n )$$
\includegraphics[max width=\textwidth, alt={}, center]{e878227b-d625-4ef2-ac49-a9dc05c5321a-27_106_68_2615_1877}
\end{enumerate}
\hfill \mbox{\textit{Edexcel C12 2014 Q11 [8]}}