Three distinct integers a, b and c satisfy the following three conditions:
- a b c=17955,
- a, b and c form an arithmetic sequence in that order, and
- (3 a+b),(3 b+c), and (3 c+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.)
Answer Choices
A. -64
B. -42
C. -68\:229
D. -48
E. 81