| Exam Board | OCR MEI |
|---|---|
| Module | C2 (Core Mathematics 2) |
| Year | 2013 |
| Session | January |
| Marks | 12 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Arithmetic Sequences and Series |
| Type | Two related arithmetic progressions |
| Difficulty | Moderate -0.3 This is a standard two-part sequences question testing routine manipulation of arithmetic and geometric progression formulas. Part (i) involves solving simultaneous equations for A and D (straightforward algebra), then calculating a partial sum. Part (ii) requires substituting into the GP sum formula and solving a quadratic in r². While it involves multiple steps and some algebraic manipulation, all techniques are standard C2 material with no novel insight required, making it slightly easier than average. |
| Spec | 1.04h Arithmetic sequences: nth term and sum formulae1.04i Geometric sequences: nth term and finite series sum |
\begin{enumerate}[label=(\roman*)]
\item An arithmetic progression has first term $A$ and common difference $D$. The sum of its first two terms is 25 and the sum of its first four terms is 250.
\begin{enumerate}[label=(\Alph*)]
\item Find the values of $A$ and $D$. [4]
\item Find the sum of the 21st to 50th terms inclusive of this sequence. [3]
\end{enumerate}
\item A geometric progression has first term $a$ and common ratio $r$, with $r \neq \pm 1$. The sum of its first two terms is 25 and the sum of its first four terms is 250.
Use the formula for the sum of a geometric progression to show that $\frac{r^4 - 1}{r^2 - 1} = 10$ and hence or otherwise find algebraically the possible values of $r$ and the corresponding values of $a$. [5]
\end{enumerate}
\hfill \mbox{\textit{OCR MEI C2 2013 Q11 [12]}}