| Exam Board | OCR |
|---|---|
| Module | H240/01 (Pure Mathematics) |
| Year | 2018 |
| Session | December |
| Marks | 10 |
| Topic | Geometric Sequences and Series |
| Type | Recursive sequence definition |
| Difficulty | Moderate -0.3 This is a straightforward geometric sequence question requiring identification of sequence type, application of the nth term formula, finite sum formula, and infinite sum formula. All parts use standard techniques with no novel problem-solving required, though part (d) involves algebraic manipulation of the infinite sum formula which elevates it slightly above pure recall. The multi-part structure and the infinite series component make it slightly easier than average overall. |
| Spec | 1.04i Geometric sequences: nth term and finite series sum1.04j Sum to infinity: convergent geometric series |r|<1 |
6 In this question you must show detailed reasoning.\\
A sequence $S$ has terms $u _ { 1 } , u _ { 2 } , u _ { 3 } \ldots$ defined by $u _ { 1 } = 500$ and $u _ { n + 1 } = 0.8 u _ { n }$.
\begin{enumerate}[label=(\alph*)]
\item State whether $S$ is an arithmetic sequence or a geometric sequence, giving a reason for your answer.
\item Find $u _ { 20 }$.
\item Find $\sum _ { n = 1 } ^ { 20 } u _ { n }$.
\item Given that $\sum _ { n = k } ^ { \infty } u _ { n } = 1024$, find the value of $k$.
\end{enumerate}
\hfill \mbox{\textit{OCR H240/01 2018 Q6 [10]}}