| Exam Board | Edexcel |
|---|---|
| Module | C12 (Core Mathematics 1 & 2) |
| Session | Specimen |
| Marks | 5 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Arithmetic Sequences and Series |
| Type | Recurrence relation: find parameter from given term |
| Difficulty | Moderate -0.3 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) with no conceptual difficulty or novel insight required, making it slightly easier than average for A-level. |
| Spec | 1.04e Sequences: nth term and recurrence relations1.04g Sigma notation: for sums of series |
7. A sequence $a _ { 1 } , a _ { 2 } , a _ { 3 } , \ldots$ is defined by
$$\begin{gathered}
a _ { 1 } = 2 \\
a _ { n + 1 } = 3 a _ { n } - c
\end{gathered}$$
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 C12 Q7 [5]}}