(a)[6]
A circle is split into $6$ sectors so that the sector angles form an arithmetic progression. The angle of the largest sector is $4$ times the angle of the smallest sector. If the circle has radius $5\,\text{cm}$, determine the perimeter of the smallest sector.
(b(i))[3]
The first, second and third terms of a geometric progression are $2k + 3$, $k + 6$ and $k$, respectively. Given that every term in the geometric progression is positive, calculate the value of the constant $k$.
(b(ii))[2]
Hence calculate the sum to infinity for the progression.