Answer:
either of {-9.5, -3.5, 2.5} or {7, 13, 19}
Step-by-step explanation:
Let x represent the first number of the arithmetic sequence. Then the second number is x+6, and the third number is x+12. The geometric sequence is then ...
(x -4), (x +5), 3(x+9)
The common ratio is then ...
(x +5)/(x -4) = 3(x +9)/(x +5)
Cross-multiplying gives ...
(x +5)² = 3(x -4)(x +9)
x² +10x +25 = 3x² +15x -108 . . . . eliminate parentheses
0 = 2x² +5x -133 . . . . . . . . . . . . . . subtract the left side
0 = (2x +19)(x -7) . . . . . . . . . . . . . . factor
x = -9.5 . . or . . 7
The possible original three numbers are ...
{-9.5, -3.5, 2.5} . . or . . {7, 13, 19}
