| Exam Board | Edexcel |
|---|---|
| Module | AEA (Advanced Extension Award) |
| Year | 2010 |
| Session | June |
| Marks | 11 |
| Paper | Download PDF ↗ |
| Topic | Arithmetic Sequences and Series |
| Type | Two related arithmetic progressions |
| Difficulty | Challenging +1.2 This is an AEA question requiring algebraic manipulation of arithmetic series formulas with symbolic parameters p and q rather than numerical values. While it demands careful algebraic work and solving simultaneous equations in terms of parameters, the approach is methodical using standard S_n = n/2[2a + (n-1)d] without requiring novel insight or proof techniques. |
| Spec | 1.04h Arithmetic sequences: nth term and sum formulae |
2.The sum of the first $p$ terms of an arithmetic series is $q$ and the sum of the first $q$ terms of the same arithmetic series is $p$ ,where $p$ and $q$ are positive integers and $p \neq q$ .
Giving simplified answers in terms of $p$ and $q$ ,find
\begin{enumerate}[label=(\alph*)]
\item the common difference of the terms in this series,
\item the first term of the series,
\item the sum of the first $( p + q )$ terms of the series.
\end{enumerate}
\hfill \mbox{\textit{Edexcel AEA 2010 Q2 [11]}}