| Exam Board | CAIE |
|---|---|
| Module | P1 (Pure Mathematics 1) |
| Year | 2010 |
| Session | June |
| Marks | 5 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Geometric Sequences and Series |
| Type | Find sum to infinity |
| Difficulty | Moderate -0.8 This is a straightforward geometric progression question requiring only direct application of standard formulas. Finding r = -1/2 from given terms is immediate, then applying the nth term formula and sum to infinity formula (which exists since |r| < 1) involves simple substitution with no problem-solving or conceptual challenges. |
| Spec | 1.04i Geometric sequences: nth term and finite series sum1.04j Sum to infinity: convergent geometric series |r|<1 |
| Answer | Marks | Guidance |
|---|---|---|
| (i) \(a = 12, ar = -6 \to r = -\frac{1}{2}\) | M1 | Attempt at \(r\) from "\(ar\)" |
| \(ar^9 = \frac{-3}{128}\) | M1 A1 | \(ar^9\) must be correct, co |
| (ii) \(S_\infty = \frac{a}{1-r}\) used \(\to 8\) | M1 A1 | Correct formula used. M1 needs \( |
| [2] |
(i) $a = 12, ar = -6 \to r = -\frac{1}{2}$ | M1 | Attempt at $r$ from "$ar$"
$ar^9 = \frac{-3}{128}$ | M1 A1 | $ar^9$ must be correct, co
(ii) $S_\infty = \frac{a}{1-r}$ used $\to 8$ | M1 A1 | Correct formula used. M1 needs $|r| < 1$
| [2] |
---1 The first term of a geometric progression is 12 and the second term is - 6 . Find\\
(i) the tenth term of the progression,\\
(ii) the sum to infinity.
\hfill \mbox{\textit{CAIE P1 2010 Q1 [5]}}