| Exam Board | Pre-U |
|---|---|
| Module | Pre-U 9794/1 (Pre-U Mathematics Paper 1) |
| Year | 2012 |
| Session | Specimen |
| Marks | 6 |
| Topic | Geometric Sequences and Series |
| Type | Find sum to infinity |
| Difficulty | Easy -1.2 This question tests routine recall and application of standard formulas. Part (i) requires substituting into the arithmetic series formula S_n = n/2(2a + (n-1)d) and solving a simple linear equation. Part (ii) is even more straightforward—direct substitution into S_∞ = a/(1-r) with given values. Both parts are textbook exercises requiring no problem-solving or insight, making this easier than average. |
| Spec | 1.04h Arithmetic sequences: nth term and sum formulae1.04j Sum to infinity: convergent geometric series |r|<1 |
**(i)** Attempt $S_{40} = \dfrac{40}{2}\{2 \times 7 + (40-1)d\}$ **M1**
Obtain correct unsimplified expression **A1**
Equate attempt at $S_{40}$ to 4960 and attempt to find $d$ **M1**
Obtain $d = 6$ **A1**
**(ii)** Attempt use of $S_\infty = \dfrac{a}{1-r}$ **M1**
Obtain $20$ **A1**
**Total: 6 marks**3 (i) In an arithmetic progression, the first term is 7 and the sum of the first 40 terms is 4960. Find the common difference.\\
(ii) A geometric progression has first term 14 and common ratio 0.3. Find the sum to infinity.
\hfill \mbox{\textit{Pre-U Pre-U 9794/1 2012 Q3 [6]}}