| Exam Board | OCR MEI |
|---|---|
| Module | C2 (Core Mathematics 2) |
| Year | 2013 |
| Session | June |
| Marks | 3 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Geometric Sequences and Series |
| Type | New GP from transformation |
| Difficulty | Moderate -0.8 This question tests basic manipulation of the geometric series sum formula S = a/(1-r). Part (i) is immediate substitution (2a/(1-r) = 2S), and part (ii) requires one algebraic step to simplify a/(1-r²) in terms of S. Both parts are routine applications with no problem-solving required, making this easier than average for A-level. |
| Spec | 1.04j Sum to infinity: convergent geometric series |r|<1 |
| Answer | Marks |
|---|---|
| \(2S\) cao | B1 |
| Answer | Marks | Guidance |
|---|---|---|
| \(\frac{a}{1-r^2}\); \(\frac{S}{1+r}\) or \(\frac{1}{1+r}S\) | M1, A1 | if M0, SC1 for \(\frac{1-r}{1-r^2} \times S\) oe |
### Part (i)
$2S$ cao | B1
### Part (ii)
$\frac{a}{1-r^2}$; $\frac{S}{1+r}$ or $\frac{1}{1+r}S$ | M1, A1 | if M0, SC1 for $\frac{1-r}{1-r^2} \times S$ oe$S$ is the sum to infinity of a geometric progression with first term $a$ and common ratio $r$.
\begin{enumerate}[label=(\roman*)]
\item Another geometric progression has first term $2a$ and common ratio $r$. Express the sum to infinity of this progression in terms of $S$. [1]
\item A third geometric progression has first term $a$ and common ratio $r^2$. Express, in its simplest form, the sum to infinity of this progression in terms of $S$ and $r$. [2]
\end{enumerate}
\hfill \mbox{\textit{OCR MEI C2 2013 Q6 [3]}}