| Exam Board | Edexcel |
|---|---|
| Module | C1 (Core Mathematics 1) |
| Year | 2011 |
| Session | January |
| Marks | 5 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Arithmetic Sequences and Series |
| Type | Recurrence relation: find parameter from given term |
| Difficulty | Moderate -0.5 This is a straightforward recurrence relation question requiring simple substitution to find a₂ and a₃, then solving a linear equation. The mechanics are routine (substitute, expand, solve), though it requires careful algebraic manipulation across multiple terms. Slightly easier than average due to the direct nature of the steps and limited conceptual demand. |
| Spec | 1.04e Sequences: nth term and recurrence relations |
| Answer | Marks |
|---|---|
| \((a_2 =)\ 6-c\) | B1 |
| (1 mark total) |
| Answer | Marks | Guidance |
|---|---|---|
| \(a_3 = 3(\text{their}\ a_2) - c\ (= 18 - 4c)\) | M1 | For attempting \(a_3\); can follow through their answer to (a) but must be an expression in \(c\) |
| \(a_1 + a_2 + a_3 = 2 + "(6-c)" + "(18-4c)"\) | M1 | For attempt to find the sum; must see evidence of sum |
| \("26 - 5c" = 0\) | A1ft | For their sum put equal to 0; follow through their values but answer must be in the form \(p + qc = 0\) |
| So \(c = 5.2\) | A1 o.a.e. | Accept any correct equivalent answer |
| (4 marks total) |
## Question 4:
### Part (a):
| $(a_2 =)\ 6-c$ | B1 | |
|(1 mark total)|||
### Part (b):
| $a_3 = 3(\text{their}\ a_2) - c\ (= 18 - 4c)$ | M1 | For attempting $a_3$; can follow through their answer to (a) but must be an expression in $c$ |
| $a_1 + a_2 + a_3 = 2 + "(6-c)" + "(18-4c)"$ | M1 | For attempt to find the sum; must see evidence of sum |
| $"26 - 5c" = 0$ | A1ft | For their sum put equal to 0; follow through their values but answer must be in the form $p + qc = 0$ |
| So $c = 5.2$ | A1 o.a.e. | Accept any correct equivalent answer |
|(4 marks total)|||
---4. A sequence $a _ { 1 } , a _ { 2 } , a _ { 3 } , \ldots$ is defined by
$$\begin{aligned}
a _ { 1 } & = 2 \\
a _ { n + 1 } & = 3 a _ { n } - c
\end{aligned}$$
where $c$ is a constant.
\begin{enumerate}[label=(\alph*)]
\item Find an expression for $a _ { 2 }$ in terms of $c$.
Given that $\sum _ { i = 1 } ^ { 3 } a _ { i } = 0$
\item find the value of $c$.
\end{enumerate}
\hfill \mbox{\textit{Edexcel C1 2011 Q4 [5]}}