| Exam Board | Edexcel |
|---|---|
| Module | FD2 (Further Decision 2) |
| Session | Specimen |
| Marks | 6 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Sequences and series, recurrence and convergence |
| Type | Recurrence relation solving for closed form |
| Difficulty | Standard +0.8 This is a standard second-order linear recurrence relation (Fibonacci sequence) requiring the auxiliary equation method to find the characteristic roots, then applying initial conditions. While systematic, it involves multiple algebraic steps including solving a quadratic with irrational roots and manipulating surds, placing it moderately above average difficulty for A-level. |
| Spec | 4.04e Line intersections: parallel, skew, or intersecting |
\begin{enumerate}
\item (a) Find the general solution of the recurrence relation
\end{enumerate}
$$u _ { n + 2 } = u _ { n + 1 } + u _ { n } , \quad n \geqslant 1$$
Given that $u _ { 1 } = 1$ and $u _ { 2 } = 1$\\
(b) find the particular solution of the recurrence relation.\\
\hfill \mbox{\textit{Edexcel FD2 Q1 [6]}}