| Exam Board | CAIE |
|---|---|
| Module | P1 (Pure Mathematics 1) |
| Year | 2015 |
| Session | June |
| Marks | 9 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Arithmetic Sequences and Series |
| Type | Arithmetic progression with parameters |
| Difficulty | Moderate -0.8 This is a straightforward two-part question testing standard arithmetic and geometric progression formulas. Part (a) requires finding n using the nth term formula then applying the sum formula—routine bookwork. Part (b)(i) uses the GP property that consecutive terms have constant ratio, leading to a simple quadratic equation, while (b)(ii) is direct application of the sum to infinity formula. All techniques are standard with no problem-solving insight required. |
| Spec | 1.04h Arithmetic sequences: nth term and sum formulae1.04i Geometric sequences: nth term and finite series sum1.04j Sum to infinity: convergent geometric series |r|<1 |
\begin{enumerate}[label=(\alph*)]
\item The first, second and last terms in an arithmetic progression are 56, 53 and $-22$ respectively. Find the sum of all the terms in the progression. [4]
\item The first, second and third terms of a geometric progression are $2k + 6$, $2k$ and $k + 2$ respectively, where $k$ is a positive constant.
\begin{enumerate}[label=(\roman*)]
\item Find the value of $k$. [3]
\item Find the sum to infinity of the progression. [2]
\end{enumerate}
\end{enumerate}
\hfill \mbox{\textit{CAIE P1 2015 Q8 [9]}}