(a)[4]
Find the possible values of the first term of a geometric progression with second term $12$ and sum to infinity $54$.
(b(i))[3]
For a progression whose $n$th term is $p + qn$, with $p$ and $q$ as constants, and where $S_n$ represents the sum of the first $n$ terms, Find an expression, in terms of $p$, $q$ and $n$, for $S_n$.
(b(ii))[2]
Given that $S_4 = 40$ and $S_6 = 72$, Find the values of $p$ and $q$.