(a) An arithmetic progression has first term \(a\) and common difference \(d\). The sum of the first 20 terms is 1100 and the sum of the first 70 terms is 14350. Find the 12th term.

(b) The first three terms of a geometric progression are \(x+6\), \(x-9\) and \(\frac12(x+1)\).

Show that \(x^2-43x+156=0\), and hence show that the sum to infinity exists for each possible value of \(x\).