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.
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 \(S _ { E }\).