| Exam Board | Edexcel |
|---|---|
| Module | C2 (Core Mathematics 2) |
| Marks | 12 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Geometric Sequences and Series |
| Type | Prove sum formula |
| Difficulty | Moderate -0.3 This is a standard C2 geometric series question with routine components: proving the sum formula (bookwork), solving simultaneous equations for a and r (straightforward algebra), and finding sum to infinity (direct formula application). While it requires multiple techniques, all are standard textbook exercises with no novel insight needed, making it slightly easier than average. |
| Spec | 1.01a Proof: structure of mathematical proof and logical steps1.04i Geometric sequences: nth term and finite series sum1.04j Sum to infinity: convergent geometric series |r|<1 |
A geometric series is $a + ar + ar^2 + \ldots$
\begin{enumerate}[label=(\alph*)]
\item Prove that the sum of the first $n$ terms of this series is given by
$$S_n = \frac{a(1-r^n)}{1-r}$$ [4]
\end{enumerate}
The second and fourth terms of the series are 3 and 1.08 respectively.
Given that all terms in the series are positive, find
\begin{enumerate}[label=(\alph*)]
\setcounter{enumi}{1}
\item the value of $r$ and the value of $a$, [5]
\item the sum to infinity of the series. [3]
\end{enumerate}
\hfill \mbox{\textit{Edexcel C2 Q6 [12]}}