Problem

An arithmetic progression has first term 2 and common difference $d$. The sum of the first $n$ terms is denoted by $S_n$.

(a) It is given that $(S_2-1)$, $S_4$, $S_9$ are the first three terms of a second arithmetic progression.

Find the value of $d$.

(b) Hence find the difference between the values of the 15th terms of the two arithmetic progressions.