| Exam Board | OCR MEI |
|---|---|
| Module | C2 (Core Mathematics 2) |
| Marks | 3 |
| 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 application of standard geometric series formulas. Given the first two terms, students simply find r = 4/5 = 0.8, then apply the sum formulas S_n = a(1-r^n)/(1-r) and S_∞ = a/(1-r). No problem-solving or conceptual insight required—pure formula recall and substitution, 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 | Guidance |
|---|---|---|
| Answer | Marks | Guidance |
| \(S_{10} = a\frac{1-r^{10}}{1-r}\); \(r = 0.8, a = 5\) | M1 | |
| \(\Rightarrow S_{10} = 5\frac{1-0.8^{10}}{0.2} = 22.32\) | A1 | [2] |
| Answer | Marks | Guidance |
|---|---|---|
| Answer | Marks | Guidance |
| \(S_\infty = a\frac{1}{1-r} = 25\) | B1 | [1] |
## Question 7:
### Part (i):
| Answer | Marks | Guidance |
|--------|-------|----------|
| $S_{10} = a\frac{1-r^{10}}{1-r}$; $r = 0.8, a = 5$ | M1 | |
| $\Rightarrow S_{10} = 5\frac{1-0.8^{10}}{0.2} = 22.32$ | A1 | **[2]** |
### Part (ii):
| Answer | Marks | Guidance |
|--------|-------|----------|
| $S_\infty = a\frac{1}{1-r} = 25$ | B1 | **[1]** |
---7 The first two terms of a geometric series are 5 and 4.\\
Find\\
(i) the sum of the first 10 terms,\\
(ii) the sum to infinity.
\hfill \mbox{\textit{OCR MEI C2 Q7 [3]}}