| Exam Board | AQA |
|---|---|
| Module | C2 (Core Mathematics 2) |
| Year | 2009 |
| Session | June |
| Marks | 11 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Geometric Sequences and Series |
| Type | Find sum to infinity |
| Difficulty | Moderate -0.3 This is a straightforward geometric series question testing standard formulas. Part (a) involves basic algebra with the nth term formula (showing r³ = 0.216), part (b) is direct substitution, part (c) applies the sum to infinity formula, and part (d) requires recognizing that the sum from n=6 onwards equals S∞ minus the first 5 terms. All techniques are routine for C2 level with no novel problem-solving required, making it slightly easier than average. |
| Spec | 1.04i Geometric sequences: nth term and finite series sum1.04j Sum to infinity: convergent geometric series |r|<1 |
A geometric series has second term $375$ and fifth term $81$.
\begin{enumerate}[label=(\alph*)]
\item \begin{enumerate}[label=(\roman*)]
\item Show that the common ratio of the series is $0.6$. [3]
\item Find the first term of the series. [2]
\end{enumerate}
\item Find the sum to infinity of the series. [2]
\item The $n$th term of the series is $u_n$. Find the value of $\sum_{n=6}^{\infty} u_n$. [4]
\end{enumerate}
\hfill \mbox{\textit{AQA C2 2009 Q7 [11]}}