| Date | November 2008 | Marks available | 4 | Reference code | 08N.1.hl.TZ0.4 |
| Level | HL only | Paper | 1 | Time zone | TZ0 |
| Command term | Find | Question number | 4 | Adapted from | N/A |
Question
An 81 metre rope is cut into n pieces of increasing lengths that form an arithmetic sequence with a common difference of d metres. Given that the lengths of the shortest and longest pieces are 1.5 metres and 7.5 metres respectively, find the values of n and d .
Markscheme
\(81 = \frac{n}{2}(1.5 + 7.5)\) M1
\( \Rightarrow n = 18\) A1
\(1.5 + 17d = 7.5\) M1
\( \Rightarrow d = \frac{6}{{17}}\) A1 N0
[4 marks]
Examiners report
There were many totally correct solutions to this question, but a number of candidates found two simultaneous equations and then spent a lot of time and working trying, often unsuccessfully, to solve these equations.
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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