Problem

(a) An arithmetic progression is such that its first term is 6 and its tenth term is 19.5.

Find the sum of the first 100 terms of this arithmetic progression.

(b) A geometric progression $a_1, a_2, a_3, \ldots$ is such that $a_1 = 24$ and the common ratio is $\frac{1}{2}$.

The sum to infinity of this geometric progression is denoted by $S$. The sum to infinity of the even-numbered terms (i.e. $a_2, a_4, a_6, \ldots$) is denoted by $S_E$.

Find the values of $S$ and $S_E$.