| Exam Board | Edexcel |
|---|---|
| Module | C1 (Core Mathematics 1) |
| Marks | 6 |
| 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 C1 recurrence relation question requiring simple substitution to find t₂ and t₃, followed by solving a quadratic equation. While it involves multiple steps, each step uses basic algebraic manipulation with no conceptual challenges beyond applying the given formula repeatedly. |
| Spec | 1.04e Sequences: nth term and recurrence relations |
| Answer | Marks | Guidance |
|---|---|---|
| (a) \(t_2 = 3k - 7\) | B1 | |
| \(t_3 = k(3k - 7) - 7 = 3k^2 - 7k - 7\) | M1 A1 | |
| (b) \(3k^2 - 7k - 7 = 13\) | ||
| \(3k^2 - 7k - 20 = 0\) | ||
| \((3k + 5)(k - 4) = 0\) | M1 | |
| \(k = -\frac{5}{3}, 4\) | A2 | (6) |
(a) $t_2 = 3k - 7$ | B1 |
$t_3 = k(3k - 7) - 7 = 3k^2 - 7k - 7$ | M1 A1 |
(b) $3k^2 - 7k - 7 = 13$ | |
$3k^2 - 7k - 20 = 0$ | |
$(3k + 5)(k - 4) = 0$ | M1 |
$k = -\frac{5}{3}, 4$ | A2 | (6)\begin{enumerate}
\item A sequence of terms $\left\{ t _ { n } \right\}$ is defined for $n \geq 1$ by the recurrence relation
\end{enumerate}
$$t _ { n + 1 } = k t _ { n } - 7 , \quad t _ { 1 } = 3$$
where $k$ is a constant.\\
(a) Find expressions for $t _ { 2 }$ and $t _ { 3 }$ in terms of $k$.
Given that $t _ { 3 } = 13$,\\
(b) find the possible values of $k$.\\
\hfill \mbox{\textit{Edexcel C1 Q5 [6]}}