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 .

$81 = \frac{n}{2}(1.5 + 7.5)$     M1

$\Rightarrow n = 18$     A1

$1.5 + 17d = 7.5$     M1

$\Rightarrow d = \frac{6}{{17}}$     A1     N0

[4 marks]

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.