(a) The first three terms of an arithmetic progression are

\(\frac1p,\quad \frac1q,\quad -\frac1q.\)

(i) Show that the common difference can be written as

\(-\frac2{3p}.\)

(ii) The \(10\)th term of the progression is \(\frac{k}{p}\), where \(k\) is a constant. Find \(k\).

(b) The sum to infinity of a geometric progression is \(8\). The second term of the progression is \(\frac32\). Find the two possible values of the common ratio.