| 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 -0.8 This is a straightforward C1 question requiring basic substitution to find terms (routine calculation), then solving simultaneous equations by comparing two consecutive terms with the recurrence relation. All steps are standard with no problem-solving insight needed, making it easier than average but not trivial due to the algebraic manipulation required in part (b). |
| Spec | 1.04e Sequences: nth term and recurrence relations |
| Answer | Marks | Guidance |
|---|---|---|
| (a) | \(1, 7, 25, 79\) | B2 |
| (b) | \(7 = a + b\) | M1 |
| \(25 = 7a + b\) | A1 | |
| subtracting, \(6a = 18\) | M1 | |
| \(a = 3, b = 4\) | A1 | (6) |
(a) | $1, 7, 25, 79$ | B2 |
(b) | $7 = a + b$ | M1 |
| $25 = 7a + b$ | A1 |
| subtracting, $6a = 18$ | M1 |
| $a = 3, b = 4$ | A1 | (6)A sequence of terms is defined by
$$u_n = 3^n - 2, \quad n \geq 1.$$
\begin{enumerate}[label=(\alph*)]
\item Write down the first four terms of the sequence. [2]
\end{enumerate}
The same sequence can also be defined by the recurrence relation
$$u_{n+1} = au_n + b, \quad n \geq 1, \quad u_1 = 1,$$
where $a$ and $b$ are constants.
\begin{enumerate}[label=(\alph*)]
\setcounter{enumi}{1}
\item Find the values of $a$ and $b$. [4]
\end{enumerate}
\hfill \mbox{\textit{Edexcel C1 Q4 [6]}}