| Date | May 2012 | Marks available | 4 | Reference code | 12M.1.hl.TZ1.1 |
| Level | HL only | Paper | 1 | Time zone | TZ1 |
| Command term | Find | Question number | 1 | Adapted from | N/A |
Question
Find the value of k if \({\sum\limits_{r = 1}^\infty{k\left( {\frac{1}{3}} \right)}^r} = 7\).
Markscheme
\({u_1} = \frac{1}{3}k{\text{ , }}r = \frac{1}{3}\) (A1) (A1)
\(7 = \frac{{\frac{1}{3}k}}{{1 - \frac{1}{3}}}\) M1
\(k = 14\) A1
[4 marks]
Examiners report
The question was well done generally. Those that did make mistakes on the question usually had the first term wrong, but did understand to use the formula for an infinite geometric series.
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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