Edexcel C12 Specimen — Question 7 5 marks

Exam BoardEdexcel
ModuleC12 (Core Mathematics 1 & 2)
SessionSpecimen
Marks5
PaperDownload PDF ↗
Mark schemeDownload PDF ↗
TopicArithmetic Sequences and Series
TypeRecurrence relation: find parameter from given term
DifficultyModerate -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.
Spec1.04e 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.
  1. Find an expression for \(a _ { 2 }\) in terms of \(c\). Given that \(\sum _ { i = 1 } ^ { 3 } a _ { i } = 0\)
  2. find the value of \(c\).

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]}}