| Exam Board | CAIE |
|---|---|
| Module | P1 (Pure Mathematics 1) |
| Year | 2004 |
| Session | June |
| Marks | 4 |
| 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 the sum to infinity formula S∞ = a/(1-r). Part (i) requires simple algebraic manipulation to find r, and part (ii) is direct substitution into the sum formula. Both parts are routine recall with minimal problem-solving, 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 |
|---|---|
| M1 A1 [2] | Use of correct formula; Correct only |
| Answer | Marks |
|---|---|
| M1 A1 [2] | Use of correct formula – \(0.75^{10}\) not \(0.75^9\); Correct only |
**(i)** $a/(1-r) = 256$ and $a = 64$ → $r = 3/4$
| M1 A1 [2] | Use of correct formula; Correct only |
**(ii)** $S_{10} = 64(1-0.75^{10})(1-0.75)$ → $S_{10} = 242$
| M1 A1 [2] | Use of correct formula – $0.75^{10}$ not $0.75^9$; Correct only |
---1 A geometric progression has first term 64 and sum to infinity 256. Find\\
(i) the common ratio,\\
(ii) the sum of the first ten terms.
\hfill \mbox{\textit{CAIE P1 2004 Q1 [4]}}