| Exam Board | SPS |
|---|---|
| Module | SPS SM (SPS SM) |
| Year | 2023 |
| Session | October |
| Marks | 9 |
| Topic | Arithmetic Sequences and Series |
| Type | Find n given sum condition |
| Difficulty | Moderate -0.3 This is a straightforward arithmetic sequence question requiring basic recall and standard techniques. Parts (i)-(iii) are trivial (iterating a recurrence, identifying linear form, naming sequence type). Part (iv) requires manipulating sums of arithmetic sequences but uses standard formulas with simple algebra—slightly below average difficulty overall. |
| Spec | 1.04e Sequences: nth term and recurrence relations1.04h Arithmetic sequences: nth term and sum formulae |
A sequence $u_1, u_2, u_3, \ldots$ is defined by
$$u_1 = 8 \quad \text{and} \quad u_{n+1} = u_n + 3.$$
\begin{enumerate}[label=(\roman*)]
\item Show that $u_5 = 20$. [1]
\item The $n$th term of the sequence can be written in the form $u_n = pn + q$. State the values of $p$ and $q$. [2]
\item State what type of sequence it is. [1]
\item Find the value of $N$ such that $\sum_{n=1}^{2N} u_n - \sum_{n=1}^{N} u_n = 1256$. [5]
\end{enumerate}
\hfill \mbox{\textit{SPS SPS SM 2023 Q5 [9]}}