| Exam Board | SPS |
|---|---|
| Module | SPS SM (SPS SM) |
| Year | 2022 |
| Session | October |
| Marks | 6 |
| Topic | Arithmetic Sequences and Series |
| Type | Find term or common difference |
| Difficulty | Moderate -0.8 This is a straightforward arithmetic series question requiring standard formula application. Part (a) uses S_n = n/2(2a + (n-1)d) with given values, yielding the result through simple algebra. Part (b) sets up a second equation from the term condition (a+7d = (a+6d)/2) and solves simultaneous equations. Both parts are routine textbook exercises with no problem-solving insight required, making this easier than average. |
| Spec | 1.04h Arithmetic sequences: nth term and sum formulae |
An arithmetic series has first term $a$ and common difference $d$.
Given that the sum of the first 9 terms is 54
\begin{enumerate}[label=(\alph*)]
\item show that
$$a + 4d = 6$$ [2]
\end{enumerate}
Given also that the 8th term is half the 7th term,
\begin{enumerate}[label=(\alph*)]
\setcounter{enumi}{1}
\item find the values of $a$ and $d$. [4]
\end{enumerate}
\hfill \mbox{\textit{SPS SPS SM 2022 Q6 [6]}}