| Exam Board | OCR |
|---|---|
| Module | H240/02 (Pure Mathematics and Statistics) |
| Year | 2018 |
| Session | December |
| Marks | 8 |
| Topic | Geometric Sequences and Series |
| Type | Sum of first n terms |
| Difficulty | Moderate -0.8 This is a straightforward geometric series question requiring only standard formula application. Parts (a) and (b) involve simple equation solving (2^n = 1024, finding integer factors), while part (c) requires slightly more thought to find non-integer r_3 but still uses the standard sum formula. All techniques are routine for Stats 1 level with no novel problem-solving required. |
| Spec | 1.04i Geometric sequences: nth term and finite series sum |
| First term | Common ratio | Number of terms | Last term | |
| Series 1 | 1 | 2 | \(n_1\) | 1024 |
| Series 2 | 1 | \(r_2\) | \(n_2\) | 1024 |
| Series 3 | 1 | \(r_3\) | \(n_3\) | 1024 |
The table shows information about three geometric series. The three geometric series have different common ratios.
\begin{center}
\begin{tabular}{|c|c|c|c|c|}
\hline
& First term & Common ratio & Number of terms & Last term \\
\hline
Series 1 & 1 & 2 & $n_1$ & 1024 \\
\hline
Series 2 & 1 & $r_2$ & $n_2$ & 1024 \\
\hline
Series 3 & 1 & $r_3$ & $n_3$ & 1024 \\
\hline
\end{tabular}
\end{center}
\begin{enumerate}[label=(\alph*)]
\item Find $n_1$. [2]
\item Given that $r_2$ is an integer less than 10, find the value of $r_2$ and the value of $n_2$. [2]
\item Given that $r_3$ is not an integer, find a possible value for the sum of all the terms in Series 3. [4]
\end{enumerate}
\hfill \mbox{\textit{OCR H240/02 2018 Q6 [8]}}