| Exam Board | Edexcel |
|---|---|
| Module | C1 (Core Mathematics 1) |
| Year | 2012 |
| Session | June |
| Marks | 7 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Arithmetic Sequences and Series |
| Type | Recurrence relation: find parameter from given term |
| Difficulty | Moderate -0.3 This is a straightforward recurrence relation question requiring simple substitution and algebraic manipulation. Parts (a) and (b) involve direct application of the formula, while part (c) requires summing four terms and solving a linear inequality—all routine C1 techniques with no novel problem-solving required. |
| Spec | 1.02g Inequalities: linear and quadratic in single variable1.04e Sequences: nth term and recurrence relations |
5. A sequence of numbers $a _ { 1 } , a _ { 2 } , a _ { 3 } \ldots$ is defined by
$$\begin{aligned}
& a _ { 1 } = 3 \\
& a _ { n + 1 } = 2 a _ { n } - c \quad ( n \geqslant 1 )
\end{aligned}$$
where $c$ is a constant.
\begin{enumerate}[label=(\alph*)]
\item Write down an expression, in terms of $c$, for $a _ { 2 }$
\item Show that $a _ { 3 } = 12 - 3 c$
Given that $\sum _ { i = 1 } ^ { 4 } a _ { i } \geqslant 23$
\item find the range of values of $c$.
\end{enumerate}
\hfill \mbox{\textit{Edexcel C1 2012 Q5 [7]}}