| Exam Board | Pre-U |
|---|---|
| Module | Pre-U 9794/1 (Pre-U Mathematics Paper 1) |
| Year | 2012 |
| Session | June |
| Marks | 5 |
| 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 (i) requires substituting into S_n = a(1-r^n)/(1-r), and part (ii) uses S_∞ = a/(1-r). Both are direct recall with simple arithmetic—easier than average A-level questions which typically require more problem-solving or multi-step reasoning. |
| Spec | 1.04i Geometric sequences: nth term and finite series sum1.04j Sum to infinity: convergent geometric series |r|<1 |
**Part (i)**
- Use of correct sum formula: M1
- Obtain correct unsimplified form $\frac{16(1 - 0.8^{12})}{1 - 0.8}$: A1
- Obtain 74.5 or rounding to 74.5 but not 74 or 75 (74.50244): A1 **[3]**
**Part (ii)**
- Use correct formula: M1
- Obtain 80: A1 **[2]**
**[Total: 5]**1 The first term of a geometric progression is 16 and the common ratio is 0.8 .\\
(i) Calculate the sum of the first 12 terms.\\
(ii) Find the sum to infinity.
\hfill \mbox{\textit{Pre-U Pre-U 9794/1 2012 Q1 [5]}}