| Exam Board | Edexcel |
|---|---|
| Module | C2 (Core Mathematics 2) |
| Marks | 12 |
| Paper | Download PDF ↗ |
| Topic | Geometric Sequences and Series |
| Type | Prove sum formula |
| Difficulty | Moderate -0.3 This is a standard C2 geometric series question testing routine techniques: deriving the sum formula (bookwork proof), solving simultaneous equations from given terms, and finding sum to infinity. While multi-part with 12 marks total, each component is straightforward textbook material requiring no novel insight—slightly easier than average due to the mechanical nature of the tasks. |
| Spec | 1.04i 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 Q16 [12]}}