In an arithmetic progression, the sum of the first ten terms is equal to the sum of the next five terms. The first term is \(a\).
Show that the common difference of the progression is \(\frac { 1 } { 3 } a\).
Given that the tenth term is 36 more than the fourth term, find the value of \(a\).
The sum to infinity of a geometric progression is 9 times the sum of the first four terms. Given that the first term is 12 , find the value of the fifth term.