(a(i))[3]
In a geometric progression, every term is positive, the second term is $24$ and the fourth term is $13\frac{1}{2}$. Determine the first term.
(a(ii))[2]
Determine the sum to infinity of the progression.
(b)[4]
A circle is split into $n$ sectors so that the sector angles form an arithmetic progression. The two smallest angles are $3^\circ$ and $5^\circ$. Determine the value of $n$.