| Exam Board | CAIE |
|---|---|
| Module | P1 (Pure Mathematics 1) |
| Year | 2011 |
| Session | November |
| Marks | 4 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Arithmetic Sequences and Series |
| Type | Mixed arithmetic and geometric |
| Difficulty | Easy -1.2 This is a straightforward application of standard formulas for arithmetic and geometric series. Given the first two terms explicitly, students simply identify the common difference/ratio and substitute into memorized sum formulas (S_n = n/2(2a + (n-1)d) and S_n = a(r^n - 1)/(r-1)). No problem-solving or conceptual insight required—pure formula recall and basic arithmetic. |
| Spec | 1.04h Arithmetic sequences: nth term and sum formulae1.04i Geometric sequences: nth term and finite series sum |
| Answer | Marks | Guidance |
|---|---|---|
| (i) \(\frac{5[8+9 \times 4]}{220}\) | M1, A1 [2] | Use correct formula with \(a=4, d=4\) |
| Answer | Marks | Guidance |
|---|---|---|
| \(4092\) | M1, A1 [2] | Use correct formula with \(a=4, r=2\) or \(\frac{1}{2}\); 4090 without 4092 A0 |
**(i)** $\frac{5[8+9 \times 4]}{220}$ | M1, A1 [2] | Use correct formula with $a=4, d=4$
**(ii)** $\frac{4(2^{10}-1)}{2-1}$
$4092$ | M1, A1 [2] | Use correct formula with $a=4, r=2$ or $\frac{1}{2}$; 4090 without 4092 A0
---The first and second terms of a progression are 4 and 8 respectively. Find the sum of the first 10 terms given that the progression is
\begin{enumerate}[label=(\roman*)]
\item an arithmetic progression, [2]
\item a geometric progression. [2]
\end{enumerate}
\hfill \mbox{\textit{CAIE P1 2011 Q2 [4]}}