In an arithmetic progression, the total of the first ten terms is the same as the total of the next five terms. The first term is $a$.
(a(i))[4]
Show that the progression has common difference $\frac{1}{3}a$.
(a(ii))[2]
Given that the tenth term is $36$ more than the fourth term, find the value of $a$.
(b)[4]
The sum to infinity of a geometric progression is $9$ times the sum of the first four terms. If the first term is $12$, find the value of the fifth term.
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