| Exam Board | SPS |
|---|---|
| Module | SPS SM (SPS SM) |
| Year | 2022 |
| Session | October |
| Marks | 11 |
| Topic | Geometric Sequences and Series |
| Type | Find year when threshold exceeded |
| Difficulty | Moderate -0.3 This is a straightforward geometric series question testing standard formulas (sum to infinity, nth term, sum of n terms, and solving an inequality). Part (a) is given as 'show that' making it routine, and all parts require direct application of memorized formulas with minimal problem-solving. Slightly easier than average due to the scaffolded structure and computational nature. |
| Spec | 1.04i Geometric sequences: nth term and finite series sum1.04j Sum to infinity: convergent geometric series |r|<1 |
The first term of a geometric series is 120. The sum to infinity of the series is 480.
\begin{enumerate}[label=(\alph*)]
\item Show that the common ratio, $r$, is $\frac{3}{4}$. [3]
\item Find, to 2 decimal places, the difference between the 5th and 6th term. [2]
\item Calculate the sum of the first 7 terms. [2]
\end{enumerate}
The sum of the first $n$ terms of the series is greater than 300.
\begin{enumerate}[label=(\alph*)]
\setcounter{enumi}{3}
\item Calculate the smallest possible value of $n$. [4]
\end{enumerate}
\hfill \mbox{\textit{SPS SPS SM 2022 Q5 [11]}}