2015 Fermat Problem 22

Three distinct integers a, b and c satisfy the following three conditions:

- abc = 17\,955, - a, b and c form an arithmetic sequence in that order, and - (3a + b), (3b + c), and (3c + a) form a geometric sequence in that order.

What is the value of a + b + 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 non-zero constant. For example, 3, 6, 12 is a geometric sequence with three terms.)

\textbf{(A)}\ -63\quad \textbf{(B)}\ -42\quad \textbf{(C)}\ -68\,229\quad \textbf{(D)}\ -48\quad \textbf{(E)}\ 81

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