(a)[4]
In an arithmetic progression whose first term is $6$ and whose tenth term is $19.5$, determine the sum of the first $100$ terms of this arithmetic progression.
(b)[4]
A geometric progression $a_1, a_2, a_3, \dots$ has first term $a_1 = 24$ and common ratio $\frac{1}{2}$. The sum to infinity of this geometric progression is called $S$. The sum to infinity of the even-numbered terms ($a_2, a_4, a_6, \dots$) is called $S_E$. Determine the values of $S$ and $S_E$.