| Exam Board | Edexcel |
|---|---|
| Module | C2 (Core Mathematics 2) |
| Year | 2012 |
| Session | January |
| Marks | 6 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Geometric Sequences and Series |
| Type | Find sum to infinity |
| Difficulty | Easy -1.2 This is a straightforward application of standard geometric series formulas with all values given directly. Part (a) uses nth term formula, (b) uses finite sum formula, and (c) uses sum to infinity formula—all routine recall with calculator work. No problem-solving or conceptual insight required, making it easier than average. |
| Spec | 1.04i Geometric sequences: nth term and finite series sum1.04j Sum to infinity: convergent geometric series |r|<1 |
| Answer | Marks | Guidance |
|---|---|---|
| Working | Marks | Guidance |
| Uses \(360 \times \left(\frac{7}{8}\right)^{19}\), to obtain 28.5 | M1, A1 (2) | M1: Correct use of formula with power = 19. A1: Accept 28.47, 28.474, or 28.47446075 |
| Answer | Marks | Guidance |
|---|---|---|
| Working | Marks | Guidance |
| Uses \(S = \frac{360(1-(\frac{7}{8})^{20})}{1-\frac{7}{8}}\), or \(S = \frac{360((\frac{7}{8})^{20}-1)}{\frac{7}{8}-1}\), to obtain 2680 | M1, A1 (2) | M1: Correct use of formula with \(n=20\). A1: Accept 2681, 2680.7, 2680.68, 2680.679, or 2680.678775. N.B. 2680.67 or 2680.0 is A0 |
| Answer | Marks | Guidance |
|---|---|---|
| Working | Marks | Guidance |
| Uses \(S = \frac{360}{1-\frac{7}{8}}\), to obtain 2880 | M1, A1cao (2) | M1: Correct use of formula. A1: Accept 2880 only |
# Question 1:
## Part (a)
| Working | Marks | Guidance |
|---------|-------|----------|
| Uses $360 \times \left(\frac{7}{8}\right)^{19}$, to obtain 28.5 | M1, A1 (2) | M1: Correct use of formula with power = 19. A1: Accept 28.47, 28.474, or 28.47446075 |
## Part (b)
| Working | Marks | Guidance |
|---------|-------|----------|
| Uses $S = \frac{360(1-(\frac{7}{8})^{20})}{1-\frac{7}{8}}$, or $S = \frac{360((\frac{7}{8})^{20}-1)}{\frac{7}{8}-1}$, to obtain 2680 | M1, A1 (2) | M1: Correct use of formula with $n=20$. A1: Accept 2681, 2680.7, 2680.68, 2680.679, or 2680.678775. N.B. 2680.67 or 2680.0 is **A0** |
## Part (c)
| Working | Marks | Guidance |
|---------|-------|----------|
| Uses $S = \frac{360}{1-\frac{7}{8}}$, to obtain 2880 | M1, A1cao (2) | M1: Correct use of formula. A1: Accept 2880 only |
---\begin{enumerate}
\item A geometric series has first term $a = 360$ and common ratio $r = \frac { 7 } { 8 }$
\end{enumerate}
Giving your answers to 3 significant figures where appropriate, find\\
(a) the 20 th term of the series,\\
(b) the sum of the first 20 terms of the series,\\
(c) the sum to infinity of the series.\\
\hfill \mbox{\textit{Edexcel C2 2012 Q1 [6]}}