, 2008

The numbers $a, b, c$, in that order, form a three term arithmetic sequence (see below) and $a + b + c = 60$. The numbers $a-2, b, c+3$, in that order, form a three term geometric sequence. Determine all possible values of $a$, $b$ and $c$. (An arithmetic sequence is a sequence in which each term after the first is obtained from the previous term by adding a constant. For example, $3, 5, 7$ is an arithmetic sequence with three terms. A geometric sequence is a sequence in which each term after the first is obtained from the previous term by multiplying it by a constant. For example, $3, 6, 12$ is a geometric sequence with three terms.)