| Exam Board | CAIE |
|---|---|
| Module | P1 (Pure Mathematics 1) |
| Year | 2018 |
| Session | November |
| Marks | 5 |
| 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 two-part question requiring only direct application of standard formulas. Part (i) uses the arithmetic series sum formula with easily calculated common difference d=-4. Part (ii) uses the geometric series sum to infinity formula with r=1/3, which is clearly less than 1. Both parts are routine recall with minimal problem-solving, making this easier than average. |
| Spec | 1.04h Arithmetic sequences: nth term and sum formulae1.04i Geometric sequences: nth term and finite series sum1.04j Sum to infinity: convergent geometric series |r|<1 |
| Answer | Marks | Guidance |
|---|---|---|
| Answer | Marks | Guidance |
| \(S_{80} = \frac{80}{2}[12 + 79 \times (-4)]\) or \(\frac{80}{2}[6+l], l = -310\) | M1A1 | Correct formula (M1). Correct \(a\), \(d\) and \(n\) (A1) |
| \(-12160\) | A1 | |
| Total: 3 |
| Answer | Marks | Guidance |
|---|---|---|
| Answer | Marks | Guidance |
| \(S_\infty = \frac{6}{1-\frac{1}{3}} = 9\) | M1A1 | Correct formula with \( |
| Total: 2 |
## Question 4:
**Part (i):**
| Answer | Marks | Guidance |
|--------|-------|----------|
| $S_{80} = \frac{80}{2}[12 + 79 \times (-4)]$ or $\frac{80}{2}[6+l], l = -310$ | M1A1 | Correct formula (M1). Correct $a$, $d$ and $n$ (A1) |
| $-12160$ | A1 | |
| | **Total: 3** | |
**Part (ii):**
| Answer | Marks | Guidance |
|--------|-------|----------|
| $S_\infty = \frac{6}{1-\frac{1}{3}} = 9$ | M1A1 | Correct formula with $|r| < 1$ for M1 |
| | **Total: 2** | |
---4 The first term of a series is 6 and the second term is 2 .\\
(i) For the case where the series is an arithmetic progression, find the sum of the first 80 terms.\\
(ii) For the case where the series is a geometric progression, find the sum to infinity.\\
\hfill \mbox{\textit{CAIE P1 2018 Q4 [5]}}