| Exam Board | SPS |
|---|---|
| Module | SPS SM (SPS SM) |
| Year | 2022 |
| Session | October |
| Marks | 7 |
| Topic | Arithmetic Sequences and Series |
| Type | Real-world AP: find term or total |
| Difficulty | Moderate -0.8 This is a straightforward arithmetic sequence problem requiring only standard formulas. Students must find the first term using two given terms (2000 and 2010), then calculate the sum. The context is clear, the method is routine, and it's a typical textbook exercise with no conceptual challenges beyond applying memorized formulas. |
| Spec | 1.04g Sigma notation: for sums of series1.04h Arithmetic sequences: nth term and sum formulae |
A 25-year programme for building new houses began in Core Town in the year 1986 and finished in the year 2010.
The number of houses built each year form an arithmetic sequence. Given that 238 houses were built in the year 2000 and 108 were built in the year 2010, find
\begin{enumerate}[label=(\alph*)]
\item the number of houses built in 1986, the first year of the building programme, [5]
\item the total number of houses built in the 25 years of the programme. [2]
\end{enumerate}
\hfill \mbox{\textit{SPS SPS SM 2022 Q3 [7]}}