| Exam Board | SPS |
|---|---|
| Module | SPS SM Pure (SPS SM Pure) |
| Year | 2021 |
| Session | June |
| Marks | 6 |
| Topic | Arithmetic Sequences and Series |
| Type | Mixed arithmetic and geometric |
| Difficulty | Moderate -0.8 This is a straightforward application of arithmetic and geometric sequence formulas with minimal problem-solving required. Part (a) uses the standard arithmetic sequence formula to find the middle term given first and last terms. Part (b) similarly applies the geometric sequence formula. Both parts are direct substitution into well-known formulas with simple arithmetic, making this easier than average A-level questions which typically require multi-step reasoning or integration of multiple concepts. |
| Spec | 1.04h Arithmetic sequences: nth term and sum formulae1.04i Geometric sequences: nth term and finite series sum |
A car has six forward gears.
The fastest speed of the car
• in 1st gear is 28 km h⁻¹
• in 6th gear is 115 km h⁻¹
Given that the fastest speed of the car in successive gears is modelled by an arithmetic sequence,
\begin{enumerate}[label=(\alph*)]
\item find the fastest speed of the car in 3rd gear. [3]
\end{enumerate}
Given that the fastest speed of the car in successive gears is modelled by a geometric sequence,
\begin{enumerate}[label=(\alph*)]
\setcounter{enumi}{1}
\item find the fastest speed of the car in 5th gear. [3]
\end{enumerate}
\hfill \mbox{\textit{SPS SPS SM Pure 2021 Q5 [6]}}