| Exam Board | Edexcel |
|---|---|
| Module | C1 (Core Mathematics 1) |
| Marks | 5 |
| Paper | Download PDF ↗ |
| Topic | Sequences and Series |
| Type | First-Order Linear Recurrence Relations |
| Difficulty | Easy -1.2 This is a straightforward recurrence relation question requiring only direct substitution to find terms and simple addition to sum them. Part (a) involves two iterations of the formula, and part (b) requires calculating two more terms and adding five numbers. No problem-solving insight or advanced techniques needed—purely mechanical application of a given formula. |
| Spec | 1.04e Sequences: nth term and recurrence relations1.04g Sigma notation: for sums of series |
A sequence $a_1, a_2, a_3, \ldots$ is defined by
$$a_1 = 3,$$
$$a_{n+1} = 3a_n - 5, \quad n \geq 1.$$
\begin{enumerate}[label=(\alph*)]
\item Find the value $a_2$ and the value of $a_3$. [2]
\item Calculate the value of $\sum_{r=1}^5 a_r$. [3]
\end{enumerate}
\hfill \mbox{\textit{Edexcel C1 Q4 [5]}}