| Date | None Specimen | Marks available | 5 | Reference code | SPNone.2.hl.TZ0.2 |
| Level | HL only | Paper | 2 | Time zone | TZ0 |
| Command term | Find | Question number | 2 | Adapted from | N/A |
Question
The first term and the common ratio of a geometric series are denoted, respectively, by a and r where a , \(r \in \mathbb{Q}\). Given that the third term is 9 and the sum to infinity is 64, find the value of a and the value of r .
Markscheme
we are given that \(a{r^2} = 9\) and \(\frac{a}{{1 - r}} = 64\) A1
dividing, \({r^2}(1 - r) = \frac{9}{{64}}\) M1
\(64{r^3} - 64{r^2} + 9 = 0\) A1
\(r = 0.75,{\text{ }}a = 16\) A1A1
[5 marks]
Examiners report
[N/A]
Syllabus sections
Topic 1 - Core: Algebra » 1.1 » Arithmetic sequences and series; sum of finite arithmetic series; geometric sequences and series; sum of finite and infinite geometric series.
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