| Exam Board | Edexcel |
|---|---|
| Module | C2 (Core Mathematics 2) |
| Marks | 10 |
| Paper | Download PDF ↗ |
| Topic | Geometric Sequences and Series |
| Type | Find sum to infinity |
| Difficulty | Standard +0.3 This is a straightforward C2 geometric series question requiring standard formula application. Part (a) uses the sum to infinity formula with given values, parts (b-c) apply standard GP formulas, and part (d) requires simple algebraic manipulation. While it has multiple parts, each step follows directly from textbook methods with no novel insight needed, 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 first term 1200. Its sum to infinity is 960.
\begin{enumerate}[label=(\alph*)]
\item Show that the common ratio of the series is $-\frac{1}{4}$. [3]
\item Find, to 3 decimal places, the difference between the ninth and tenth terms of the series. [3]
\item Write down an expression for the sum of the first $n$ terms of the series. [2]
\end{enumerate}
Given that $n$ is odd,
\begin{enumerate}[label=(\alph*)]
\setcounter{enumi}{3}
\item prove that the sum of the first $n$ terms of the series is
$$960(1 + 0.25^n).$$ [2]
\end{enumerate}
\hfill \mbox{\textit{Edexcel C2 Q37 [10]}}